You can own an AR 15 like that in NJ. You can have a muzzle brake or compensator on the barrel, it must be permanently attached. You can not have a flash hider. A collapsible stock must be pinned to one position. 15rd mags or less. Barrel length no less than 16" (including compensator). No bayonet lug.
Here is a pic of a NJ compliant DPMS AP4 Carbine with carry handle and without: