First, do you have ROOM at the top to raise the sail?
What you are seeing is NORMAL for a high performance
genoa. These
sails are optimized for close hauled
work, and are called "deck sweepers" for good reason. Having the foot of the sail right down literal touching the
deck when sheeted in tight greatly improves windward performance. If you want to see pictures, just
google "j-24
genoa images".
For the casual cruiser, however, they can be way more trouble than they are worth. For one thing, on other points of sail they tend to wear and chafe (as you observe!). They can get hung up on rails and stanchions while sheeting in. They also severely restrict visibility, and with a short-handed crew without an extra pair of eyes to constantly scan to leeward this can be a very real
safety issue.
If this is a true deck-sweeping genoa it is unlikely that simply raising it up will give you a useful sail. You might be challenged to find a point far enough aft to lead the sheet to get anything like the appropriate twist in the leech.