I think a stock E90x is suppose to be rated at somewhere in the range of 13.3-13.9s. It's a huge range but allows for weight differences.
For example, being an E93 I'd probably run similar times to you stock due to the extra weight. If you are AT you may also yield a slower time than an MT.
Btw, 27 is HOT and I bet you did t consider relative humidity and how bad the weather has been. This air is gross and I bet it ain't helping our engines much either.
Try brake boosting as mentioned and you should be able to break 13's.
When is the next open track day btw? I'd definitely be interested in going too!!
I wanna run stock and then JB4 and compare