Star jasmine (Trachelospermum jasminoides) will thrive in part shade. May eventually get taller than your limit but will benefit from being sheared back annually anyway. Otherwise liriope or dwarf mondo grass will work well, also ajuga and both Vinca major and minor. Of these choices, the jasmine will produce flowers over the longest period and fragrant ones as well.

I'm in zone 4. Any suggestions on good ground cover for part sun in Minnesota? Thanks.