387F

Tools print 387F as "power management: standby current violation", and some as closed-circuit current. A forum reply explains it as something not turning off when the car is asleep, so the draw is higher than the car expects in that mode, with aftermarket equipment or a module that no longer sleeps as the usual suspects. That is a reply, not a BMW document.

One E90Post owner started getting 387F and an "increase battery output" message after installing a Bluetooth module for his tuning box; the car always started, even after sitting for weeks, and he later wrote that he changed the power feed to the Bluetooth unit and the code went away. Another poster had suggested a source that is live only with the ignition, and the owner replied his was already wired as instructed, under the big fuse. An X1 35i owner got the code with a wireless tuning adapter left plugged in, and a reply in a second thread says an adapter left in the OBD port is always powered and will trigger it.

Other cases in the same threads: a 335i that started throwing it after its headlights were replaced following a fender bender (the car had run the same tuning box with Bluetooth for years without it), and a 135i whose owner reports hard starting after two days, revs dropping and stalling until he pressed the accelerator, with 387F appearing as it warmed up. An E84 X1 owner has had it stored since buying the car and tops up the battery with a CTEK every few weeks.

One Q&A answer reads 387F as a boost-related information code and blames a stuck blow-off valve. It is the only source in this set that connects it to the turbo; the threads are about current draw.