I saw a big increase with my 2012 28i after I changed by driving habits. I would recommend trying to drive more like an old man for a while: slow starts, more coasting to stop lights. I've been able to get 27mpg HWY and 24mpg combined on my N52. I would expect the N20 to be even better.
My wife drives a 2013 328i with N20 and she's been able to get 28 combined from the get go, so it's definitely possible. If the driving habits don't reveal any change, you might try 93 octane, just in case. Otherwise, I would have it looked at.