A floorplan or photos would be helpful if you want a precise answer. Refer to you dryers manual for maximum vent length, but typically you can extend the vent around 25-30ft to get it to an exit point. The roof is an option but less ideal. Typically a gable end of the house is best.
They also make ventless condensing dryers which are in supposed to very efficient but have long drying cycles. I’ve not heard the best reviews on them, but do your own research.
More generally speaking try to limit your dryer use. It just adds wear and tear on your clothes and costs money to use. Hang dry when you can. I personally partially dry and then hang as it makes clothes largely wrinkle free.
Edit: I see the floorplan OP uploaded, but I’m unclear on what is an exterior wall. Is the north side of the garage an exterior wall? Because that would be a short run to extend the vent to reach an exit point.