I've had noise free sound from THR10 by using phones out and connecting THR to a separate wall outlet. THR doesn't behave well with other equipment in the same outlet, it's creating some static noise.
I had an idea to record THR with a microphone using almost acoustic level output. This is where problems start, because I noticed that THR has actually quite lot of static noise and it's somehow related to grounding/power supply, because when I touch the metal parts of guitar there is less noise. Also, if you touch the metal handle of THR it's even more effective way to kill the noise. But sadly I don't have three hands. Even worse there is always an audible "pop" noise when touching metal and more you listen to it the more it starts to chew your mind.
My THR is the newer model with legendary piece of tape inside to detach some wires that apparently caused some high pitch noise. Some have fixed noise problems with another, better power supply. But it seems to be quite hard to find 15V/3A psu with proper connection cable. This far I've found 15V, but it's only 2A. Switching to new psu is also a random event, because they are all made in China. Some have even placed a noise gate pedal in front of THR. I don't think it's that good idea, because noise gate is always making the sound worse.
I guess THR is not properly shielded and the psu could be low quality. The noise source is guitar, because if tone knobs (or volume) are zeroed then there is no noise, but the sound is just too dull and boomy to be useful. I've tried different guitars so it's probably not worth the trouble to shield the guitar itself. Also, my actual guitar amp Laney Lionheart has no noise whatsoever so it's probably just the THR to blame.
Update: I can have noise free sound - with a guitar that has EMG active pickups. It's not the perfect solution, because my EMG guitar (Godin Redline) has only the bridge pickup and it's quite different sound compared to neck pickup of a single coil Fender stratocaster. But I guess it's a first world problem.