I'd say work in two steps: First try to remove the noise from the source (pickups picking up electronic noise) Try positioning yourself and the Helix away from electronic interference like computer monitors and such. I have an LED strip behind my desktop when its on it creates a lot of weird noise in surrounding audio equipment. Try a different wall outlet, grounded if possible. The power in my house seems to be wired in a way (I'm not an expert on this) that if I have a bunch of stuff connected to the same outlet via an extension cable, there seems to be some noise introduced. Try another guitar if possible, maybe the shielding on your guitar is lacking? The pups sound like humbuckers in that audio clip, amirite? Single coils are noisy beasts by nature.
Second step is mitigation, do whatever you can to minimize the noise that you can't remove: set the input gate to ON and the threshold somewhere where you can no longer hear the noise, and the decay time to short, less than 100ms, but there are no right or wrong answers how to set it correctly. Use your ears and try what sounds best. Try to lower the gain and master to reduce the noise -- this is probably a last resort fix since it alters your tone.
Another solution would be to switch to active pickups on your guitar which tend to be really quiet. Its a night and day difference at least on my Helix whether I play on actives or passives. No noise on the actives on high gain presets, on passives its always kind of present and I just use a noise gate to mitigate it.
