As far as I understand, an HTTP body may not be encoded in Base64:
HTTP does not use the Content-Transfer-Encoding (CTE) field of RFC
2045. Proxies and gateways from MIME-compliant protocols to HTTP MUST
remove any non-identity CTE ("quoted-printable" or "base64") encoding
prior to delivering the response message to an HTTP client.
Identity being:
The default (identity) encoding; the use of no transformation
whatsoever.
Of course you're allowed to transport Base64-encoded data using HTTP, but that should be something both parties (client and server) agree on, and there doesn't seem to be a header to describe this behavior.