The bearing in your supercharger pulley is going bad. When the car is idling, the supercharger clutch is disengaged and the bearing is working. When you rev up the engine the supercharger clutch engages and the bearing is no longer working. That's why the sound goes away when you rev up the engine and then comes back at idle.

Take off the serpentine belt and remove the supercharger pulley. Put a box wrench on the pulley bolt and hit it with a rubber mallet (to kind of loosen it in short bursts) while holding the supercharger pulley from turning (as best you can). When you remove that thick washer from behind the pulley bolt, make a note of it's position in relation to the painted stripe on it. You'll need to reinstall that washer in the same relative position so you can then properly re-attach and tighten the bolt to the right torque (by lining up the stripe on the bolt with the stripe on the washer).

When you get the pulley off . . . hold it with your fingers inside the bearing and spin it. You should be able to tell that the bearing is bad. Your local NAPA auto parts should be able to install a new bearing for you. If you buy the bearing from them they will probably install it at no charge. If you try to save a few bucks buying the new bearing elsewhere and then bring everything to them, they will likely charge you to change out the bearing and you'll probably end up spending more.

When you reassemble it tap the bolt tight until the painted stripe lines up with the painted stripe on the washer. That will be the correct torque for the bolt. DO NOT overtighten that bolt because it is hollow and it WILL break (giving you another problem to solve)!

I would also recommend changing the idler pulley (or eliminating it with a Needswings pulley saver kit OR a LateModel21 pulley wrap kit) because the idler pulley is a failure waiting to happen. I know you said it seemed OK but at 37K I'm sure that bearing is going bad too . . .

Report back and let us know what you find.

PS - I think you mean it has a code3 pulley and a Eurocharged tune. Eurocharged makes pulleys too but Code3 is a different brand of pulley.