There is no minor league play index (which would be the deepest rabbit hole on the internet), but here is a list of six-walk games in the majors.
Triple-A Durham Bulls (44-41)
Durham was on the wrong side of a slugfest in its 17-6 loss to Charlotte. The Knights bashed six home runs, including two grand slams. There were two mitigating factors. The Bulls committed seven errors leading to seven unearned runs, and two position players combined to finish the game. Luke Maile, Corey Brown and Nick Franklin homered for Durham, but it was not nearly enough.