Here's the specs on the 6.4's
Originally Posted by Based_on_2008_model
F-250 16,400 lbs. 5th-Wheel Towing • 12,500 lbs. Conventional Towing • 3170 lbs. Payload • 23,000 lbs. GCWR • 10,000 lbs. GVWR • 6000 lbs. Front GAWR
F-350 18,700 lbs. 5th-Wheel Towing • 15,000 lbs. Conventional Towing • 5720 lbs. Payload • 26,000 lbs. GCWR • 13,000 lbs. GVWR • 6000 lbs. Front GAWR
F-450 24,500 lbs. New Record 5th-Wheel Towing • 16,000 lbs. New Record Conventional Towing • 6120 lbs. New Record Payload • 33,000 lbs. New Record GCWR • 14,500 lbs. New Record GVWR • 6500 lbs. New Record Front GAWR*
As you can see, the F250 will not support that sized trailer unless it's a 5th wheel. The F350 will be right on the bubble but still unsafe. The only one that can safely pull that load will be the F450.
Mind you, the above numbers are based on a 2008 model, but they didn't change the payloads until 2011's came out and not for the better. You actually lose towing capacity on the 2011's and newer trucks.
Slightly Off Topic: I'd like to see a picture of that thing with your truck in front. That's gotta look crazy.