Apex HTTP PUT with Binary Data

I am trying to submit a binary file (Word doc) using HTTP/PUT, however it seems like the encoding is not properly done and it is not sending binary data, it works ok if I just send txt files...

Any way to make the data to be binary instead of encoded like strings?

EncodingUtil.base64Encode(theWordDocBlob);

Assuming your word doc is a Blob in Apex, the above will work.