How to implement the multitouch in Unity 2D?

Question

In this game there are many object that has the tag "enemy" all these enemy are instances of the same class, in this class I used the method "OnMouseDown" to handle the user's click but this is not the perfect way because it is not compatible with the multitouch

I looked around on the net and I found this solution:

public class TouchInput : MonoBehaviour {

public LayerMask touchInputMask;

private List<GameObject> touchList = new List<GameObject>();
private GameObject[] touchesOld;
private RaycastHit hit;

void update()
{
#if UNITY_EDITOR
    if (Input.GetMouseButton(1) || Input.GetMouseButtonUp(1))
    {
        touchesOld = new GameObject[touchList.Count];
        touchList.CopyTo(touchesOld);
        touchList.Clear();

            Ray ray = GetComponent<Camera>().ScreenPointToRay(Input.mousePosition);

            if (Physics.Raycast(ray, out hit, touchInputMask))
            {
                GameObject recipient = hit.transform.gameObject;
                touchList.Add(recipient);

                if (Input.GetMouseButtonDown(0))
                {
                    recipient.SendMessage("OnTouchDown", hit.point, SendMessageOptions.DontRequireReceiver);
                }
                else if (Input.GetMouseButtonUp(0))
                {
                    recipient.SendMessage("OnTouchUp", hit.point, SendMessageOptions.DontRequireReceiver);
                }
                else if (Input.GetMouseButton(0))
                {
                    recipient.SendMessage("OnTouchStay", hit.point, SendMessageOptions.DontRequireReceiver);
                }
            }
        }

        foreach (GameObject g in touchesOld)
        {
            if (!touchList.Contains(g))
            {
                g.SendMessage("OnTouchExit", hit.point, SendMessageOptions.DontRequireReceiver);
            }

        }
 #endif


    if (Input.touchCount > 0)
    {
        touchesOld = new GameObject[touchList.Count];
        touchList.CopyTo(touchesOld);
        touchList.Clear();

        foreach (Touch touch in Input.touches)
        {
            Ray ray = GetComponent<Camera>().ScreenPointToRay(touch.position);

            if(Physics.Raycast(ray, out hit, touchInputMask))
            {
                GameObject recipient = hit.transform.gameObject;
                touchList.Add(recipient);

                if(touch.phase == TouchPhase.Began)
                {
                    recipient.SendMessage("OnTouchDown", hit.point, SendMessageOptions.DontRequireReceiver);
                }
                else if (touch.phase == TouchPhase.Ended)
                {
                    recipient.SendMessage("OnTouchUp", hit.point, SendMessageOptions.DontRequireReceiver);
                }
                else if (touch.phase == TouchPhase.Stationary || touch.phase == TouchPhase.Moved)
                {
                    recipient.SendMessage("OnTouchStay", hit.point, SendMessageOptions.DontRequireReceiver);
                }
                else if (touch.phase == TouchPhase.Canceled)
                {
                    recipient.SendMessage("OnTouchExit", hit.point, SendMessageOptions.DontRequireReceiver);
                }
            }
        }

        foreach (GameObject g in touchesOld)
        {
            if (!touchList.Contains(g))
            {
                g.SendMessage("OnTouchExit", hit.point, SendMessageOptions.DontRequireReceiver);
            }
        }
    }
}

}

But I think that this solution does not work in a 2d game (I tried it, I attached this script to the main camera, there aren't any errors, but the method "update" seems to not be never called for some reasons).

Any Ideas?

UPDATE:

The code I'm using:

using System.Collections;
using System.Collections.Generic;
using UnityEngine;
using UnityEngine.EventSystems;

public class TouchInput : MonoBehaviour, IPointerDownHandler
{

    void Start()
    {
        addPhysics2DRaycaster();
    }

    void addPhysics2DRaycaster()
    {
        Physics2DRaycaster physicsRaycaster = GameObject.FindObjectOfType<Physics2DRaycaster>();
        if (physicsRaycaster == null)
        {
            Camera.main.gameObject.AddComponent<Physics2DRaycaster>();
        }
    }

    public void OnPointerDown(PointerEventData eventData)
    {
        Debug.Log("Clicked: " + eventData.pointerCurrentRaycast.gameObject.name);
    }

    //Implement Other Events from Method 1

 }

Main camera:

EventSystem:

Console: (there is only the unity ads advert)

Hierarchy:

My object: