I've got an 05 F-350 6.0, currently running syn blend from local dealer (which I plan on swapping for full syn on my next oil change) and I have the same noise but it's driver side. Just had FICM repaired by Ed at FICM Repair.com. (awesome guy, awesome job)
I've read several threads on this noise and apparently a LOT of 6.0s make this sound with no immediate negative impact. My guess would be an injector, especially on my truck, as it is closing on 140,000 miles. I'm due for new injectors all around and have has a pesky P0269 (#3 contribution balance fault) code that I can't get rid of, even after fixed FICM and replacing the #3 injector with a reman.