10 miles isn't that far so I doubt the factory antenna is the issue, it's more likely simulcast distortion. Try programming in a few analog or conventional P25 agencies that are on the opposite side of the city. If you get those fine but not the city it's likely S.D...check what you want to listen to in the database here, if you see "simulcast" you're SOL. If you see "P25E" in the mode column you're even more SOL because it's encrypted, no scanner can decode it
As for a discreet antenna, you could always put a mini mag mount type antenna meant for a vehicle in your window. I did this with decent results.