"quality" might not have been the best choice in wording, but I will say you must have a garage door that is not traditional in regard to height or construction. I have inches of clearance with our standard 7' overhead door, not the opposite like you are apparently dealing with.
To attempt to be constructive, you could look at having the tracks extended to raise the door up some. Depending on the exact type of overhead door you have, they might be able to change panels and extend tracks to raise it when it is retracted, also assuming you have clearance above it to raise it up. I'm saying all this wondering if it will be possible at all because overhead doors that are lower than normal are usually that way for a reason, usually because there isn't enough clearance above it in the first place.
You could always post some pics of the door and maybe get some ideas of how to change it, possibly....
'15 Overland Diamond Black, 3.0L Turbodiesel, Quadra-drive II