I posted the patch I made, the one that I first noticed this noise on, on the L6 Support Forums. Someone w/ whom I was corresponding w/ tried it and got that same sound, only they said not a severely as I was getting it.
I was getting the sound regardless of what amps I was using, even on clean tones.
It appears that using two noise gates in each chain was exacerbating the problem, but I had to because just using one wasn't enough to quiet the hum.
Anyways, the background hum was acting up much less than usual today, and I was able to lose one of the gates. Doing so lessened the noise i was getting considerably, but it's still there though.
I live in India so I face power cuts sometimes.
The sound you're getting is the sound I get usually when the PC is running on the UPS. Try using a different USB cable and maybe a balanced guitar cable.