Jim Bottomley and Big Hittin Mark Whiten tied for 12.
I wasn't around for the Bottomley one in 1924 so people will have to ask Wilbur about that but I do remember when Whiten hit the 4 HRs 1 game.
Interestingly when Whiten had four homeruns and 12 RBIs in one game, he immediately followed that by having only four homeruns and 12 RBIs the rest of the year