If you've never explored it in detail, you may be surprised to learn just how far a refined technique goes towards keeping noise in check, when using high gain.
Doing a pull-off and getting the slightest brush against an adjacent string from the finger you just used..., very slight overlap of notes when switching strings..., a harmonic from an open string you don't have muted, etc. All these tiny things, and more, contribute to unwanted noise.
Try this simple exercise with a high gain tone: Play a C-B-A on B/13-12 G/14. If you don't have your palm draped over the A string, and end the G with the tip of your finger resting against the D string, both the A & D string will produce a harmonic. Further, if you don't lift your finger off the B just enough to mute it at the instant you land the A, and/or don't drape the bottom of your finger over the B string as you land the A note, you can get just a millisecond of dissonant note overlap that also adds just a touch of noise.
Play those same 3 notes, but all on the B string, while making sure all the other strings are muted, and each note should sound nice and clear. If playing it the first way doesn't sound just as clear, then the noise you hear has to be dealt with via your technique.
This may not be your exact issue, but this part of your post is why I thought to mention what I posted above.