Multi-host access involves an overlay network with service discovery.
See docker/networking:
An overlay network requires a key-value store. The store maintains information about the network state which includes discovery, networks, endpoints, IP Addresses, and more.
The Docker Engine currently supports Consul, etcd, ZooKeeper (Distributed store), and BoltDB (Local store) key-value store stores.
This example uses Consul.

If if your your nodes (the other computers across the same network) runs their docker daemon with a reference to that key-value store, they will be able to communicate with containers from other nodes.
DOCKER_OPTS="-H tcp://0.0.0.0:2375 -H unix:///var/run/docker.sock --cluster-store=consul://<NODE-0-PRIVATE-IP>:8500/network --cluster-advertise=eth0:2375"
You just need to create an overlay network:
docker network create -d overlay --subnet=10.10.10.0/24 RED
(it will be available in all computers because of the key-value store)
And run your containers on that network:
docker run -itd --name container1 --net RED busybox