That's normal with my SIIIv6
With the amp turned up and the volumes up on the guitar you will get some "white noise" through the amp, what I call the noise floor.
When you start playing the volume (of the guitar through the amp) should be much louder than the white noise and it (white noise) should not be decernable while playing the guitar.
When you have the guitar plugged in and you are not touching the strings YOU are an ungrounded antennae and are causing the increased noise
Try setting the plugged in guitar on the couch and move away from it, the noise will go down, a lot.
When you touch the strings, the noise goes down because you are getting grounded through the guitar string ground.
You can try different preamp tubes, some are noticably quieter than others and will lower the noise floor, another source MAY be CC resistors in the pre-amp circuit.
Hope this helps