I see nothing in the county ordinances that supports your viewpoint. Chapter 12, Article II, Section 12.32: http://www.amlegal.com/library/nc/johnstoncounty.shtml
I think your neighbors are being kind by giving you a warning and opportunity to correct the situation. If I had to listen to a boxer bark frequently on a daily basis, I'm not sure I would have given you a warning. Have some consideration for your neighbors.
If you truly want to rectify the situation and have no other alternative, you can get a bark control collar to train him. It works like an invisible fence collar, sending him a couple of warnings and then a "correction" if he doesnt stop. They aren't expensive, somewhere around $30. Eventually he wont need it anymore. PS - I dont want to hear the peanut gallery pipe in telling me how it's cruel. This works - Instead, come up with another option.
May be barking out of boredom, wanting some family attention or to just be inside. Good active play intereaction, walks or some form of exercise should wear him down a bit. Sorry if you do all this - post was edited away so don't know full story. But I feel dogs don't usually bark unless there's a legit reason. Meaning they don't do it just to hear themselves or being annoyances - IMO anyway.
I just hope and pray that the answer doesn't result in another dog dumped on the side of the road somewhere.