Yes......just headphones and the noise sounded worse in horrific stereo.Did you try it with nothing but headphones and a guitar (no USB, no external amp, no other cables at all)?
I know this kind of thing can be very frustrating, but have no fear. If it is something with the unit itself, Fractal Support is the best in the business. They will without a doubt get you fixed up fast.
It is still there.Unplug the guitar cable from the front of your Axe-Fx. What happens to the noise?