Are the factory presets noisy aswell or is it just your presets?
Does the "clip" LED light up when you play?
In I/O button menu, check the input level of input 1 rear: if you strum hard, the red LED should just be "tickled"
In I/O button menu, check the input mode:
Input 1 left select should be set to "rear"
Input 1 mode should be set to "mono"
Output 1 mode should be set to "stereo".
The pad/boost mode should be set to 0.
Check the global amp gain (not the preset amp gain... there is a global setting affecting all presets). It should be set to 0.
Set the XLR ground lift on the back of your Axe back to off. It's currently ON from the picture. It doesn't really matter since you don't use the XLR outs, but it's saver as you might forget about it the next time you plug in analogue.
In your preset layout, go to the "Gate" tab and turn it off.
In your preset layout, go to the "output/mix" tab and check if everything is on zero.
@ Simeon: Using the rear input is perfectly fine. I only use rear and never had any noise issues.
You can download the GERMAN manual on g66.eu:
http://www.g66.eu/images/Manuals/Axe-Fx_II_Manual_DE.pdf