There are very few codes that an OBC can set before it it warm and running closed loop. Rough idle in the first couple of minutes of operation will not result in any codes unless the problem continues while the car is warm.
My wife's 330 started having rough startup around 75,000 miles. Hers sounds like it may have a leaking injector that drips when the car is off. I have not tracked down the problem yet, but she is not complaining so it has not made my priority list.