The Columbus 365RL "brochure" GVWR is 15,910 lbs. Ford says your F250/6.7 can tow 16-16,700 lbs. depending upon your truck's specific configuration. Sounds like you'd be ok, however, I find that brochure information is not always accurate.
Best way to know is weigh your truck loaded with fuel and add 200 lbs. for each driver & passenger. Then subtract this amount from your truck's GCWR to determine what your truck will pull safely. Next be sure to learn what your 365's actual unloaded weight is (found on a yellow sticker on the coach's door frame) and subtract this amount from the truck's GCWR. The difference is the weight you can add to your coach safely.
A good source of reference is; RV Camping & RV Lifestyle - Changin' Gears
Hope this helps.