I've got a late pre-LCI M135i, picked up start of March.
I have exactly the same issue and and have it booked in for the dealers to look at. That and the HK hiss! This forum is excellent, didn't want to post anything but glad to read I'm not alone.
Symptoms are: Manual or Auto mode, when in 2nd you hear this gearbox/turbo noise. In manual mode you can just hold the throttle there and it remains. It's sounds a bit like a cross of a supercharger or my old CTR had a noise from the cam chain. The high pitch whine stops about 2krpm. Slowly goes away as you go higher, say 3k. In 1st and 3rd you can just about hear something.....very very quiet.
I've noticed something else too.... It's happened a few times where i'm doing about 20mph (or once 60mph), auto mode, and I notice the car is producing a very loud high pitched noise. It's sooo high pittched that it's at the top of my hearing range (sort of feel it rather than hear it initially). I mute the radio and then realise it's there. If I accelerate (to spool turbos) it remains and stays constant. Last time it got slightly quieter after about 30 seconds, I hit a bump and it immediately stopped. It has only happened when below 2k revs for a couple of mins. Related to HK hiss or 2nd gear whine?!