Same problem here, I saw this on internet, I don't know if it works, I don't prove it yet, but...
The problem is with the piezo pickups and is very easy to fix. The plinky sound, especially, but not limited to palm muting, comes from the way the string "pings" against the piezo. What you need to do is change your strings, but on the new set, put a piece of duct tape or gaphers tape about .5" long about .25" from the ball end of the new string. This will deaden the string against the piezo and completely eliminates that "plinky" sound you are hearing. I sent my Variax back to Line 6 twice before discovering this amazing fix. IT WORKS!!!!!