Rest error message in HTTP Header or Response Body?

It is better to have error details in the body. Furthermore, many (most / almost all, eg. WSGI) servers and clients do not support changing the name of the error code - treat them as fixed pairs (so eg. 400 is always "Bad Request" and not "Bad Request - You Forgot To Specify The User ID"). Even if they won't break, they won't care about your special name for specific error code.

The error does not belong in the body. It belongs in the Warning header.

The Warning general HTTP header contains information about possible problems with the status of the message.

Reference

Quoting from the HTTP specification for 400.x error codes:

The 4xx class of status code is intended for cases in which the client seems to have erred. Except when responding to a HEAD request, the server SHOULD include an entity containing an explanation of the error situation, and whether it is a temporary or permanent condition. These status codes are applicable to any request method. User agents SHOULD display any included entity to the user.

It is best practice to include the error message as an entity in the body of the HTTP response - be it JSON, plain text, formatted HTML, or whatever other format you may want to utilize.