I can’t find mention of that one. Is it by chance the HL-3040CN? If so, doesn’t look promising:
http://www.openprinting.org/printers/manufacturer/Brother
More reading:
https://www.reddit.com/r/linux/comments/5xx49k/how_did_we_let_open_source_printing_support_get/
Old, but might be a starting point:
Might help with other Brother printers: