Ahhh the dreaded limp mode malfunction light! Unfortunately there are a whole bunch of different reasons this can activate. The first step is getting the codes read, without them anyone here is literally just guessing or going off what it was when theirs did it. I have had it pop up a few times! And yes, the turbo was one.
It would also help to know the situation when it tripped. For instance, when my wastegate went out, most of the time the car drove fine, but on the freeway when giving it just a little gas to go up an incline or speed up to pass.... not enough gas to kick the transmission down a gear, just enough to pick up a small bit of speed on an incline, bong! There it would go! That’s a pretty good symptom of the wastegate. But we need the codes first.
you can go to autozone or something like that, but the problem is that their scan tools do not read all of the codes our cars spit out. Some are proprietary BMW codes that you need specific software to read. Some of us buy our own eventually, especially if you are going to be working on it yourself, it is a necessity.
For now I would recommend making a couple of phone calls to some local Euro specialty shops and find one that will scan it for no charge, they are out there. Try to find one that does a lot of BMW/MINI vehicles and they will have something to read the codes.
then post them here and we can help narrow down the issue, so you aren’t just throwing parts at it, or getting charged for something unnecessary.
good luck