I've got a similar situation behind my garage that's 9' x 22'. I've slowly been planting excess daylilies, Queen Anne's Lace, some spare hostas back there. It really only get mid-day sun for maybe 2 hours, so I'm surprised anything has grown back there other than weeds. But it's a constant battle to keep the weeds out. Add to that from the neighbor's yard comes a wild grape vine, which is nice, but it then climbs up the garage and is hard to pull down, and it's impossible to try and walk back there to do any cleanup because you'll trip on the grape vines. I'm ready to start killing off the grape vines at this point.
The previous owners tried laying down plywood, but that's decomposing and the weeds root in the slightest crack anyway, so it really didn't do any good. I've also found old carpeting that they put down, and the weeds just root in that as well once anything starts to break down. It's an endless battle and I feel your pain about it.
