Two options: detached garage or attached garage. There are limitations based on the City of Minneapolis's building codes. Happily, there is a ton of information about this available online.
This is considered an addition to the house, rather than a garage, but it comes with a lot more crap. The good side is that it can extend to within 5 feet of the property line on any side, and there are essentially no height restrictions.
On the bad side, being attached to the house makes it a lot more expensive.
The good side: a detached garage can be within 12 inches of the property line. This makes it a lot more efficient for use of space. Bad side is that the size restrictions are a maximum of 26 x 26 feet, and a 12 foot mean roof height.
Measuring the space, the largest "addition" space that I can add is 27 x 32 feet.
It's all pipe-dreamish right now anyway. I'm just gathering data for the decision making process.