Presumably you bought it new...and reasonably recently? New Boss Katana amps come with Boss warranty by default don't they?
What you're describing sounds like either a dirty or faulty connection somewhere or EMF noise possibly from other devices on the mains circuit. e.g. Fridge or air conditioning motors.
In any case, I'd fault find myself first. Lots of process of elimination to follow here. Simplest first.
Are you using a well shielded quality instrument cable with quality connectors? i.e. Rapco Horizon with nickel Switchcraft connectors. Imperative IME. Cheap included in the box moulded terminal cables are utter rubbish and frequently a source of noise. Think of them as a big aerial for unwanted EMF throughout the home.
Is your guitar a super cheapie or ? Low quality or dirty pots, poorly soldered connectors or dodgy earths can generate noise. Cheap pickups can generate noticble hum when the volume is increased, especially with gain cranked, but not usually popping and crackling IME.
Those are the easist to either check or assess, but the most probable IMO is noise generated by something on the same circuit of your house mains power supply, or the circuit itself being dirty'. If you have a second power '(vs light) circuit, plug into that and see if it ceases. If you don't have a second circuit or it doesn't, buy a power filter (not just a surge protector) and plug your amp into that. A power strip or even single port wall wart type with true filtering capability will do.
If you're nearby any other active electronics which might be generating strong EMF, e.g. HT speakers, wi-fi routers, ceiling or pedastal fans, some types of lights, move to an area of the property as remote as you can potentially devoid of sources of interference and see how you go.
Good luck. Although it could be a fault with the Katana itself, it's unlikely (low probability). If after basic fault finding nothing evidences itself as the culprit, if you can, take it to where you bought it and ask them to test it so you can demonstrate the symptoms you are experiencing. On their mains power and with an instrument and cable different from yours, if it's still occurring, its indicative it might be a fault with the amp.