Don’t know a lot about the 114i engine but I wouldn’t think you can up a 100bhp engine to those sorts of figures. If you can get close to 200 then it’s going to cost some £££ to achieve it.
Better off just swapping car for one with bigger engine

 

From what ive found on the internet, the N13 engines are pretty strong and can handle up to 400hp. I cant seem to find what they do to get those kind of numbers though…

You can get 220-230 hp just from a stage 1 remap.- they share the same engine as the 116 and 118.


Theres a young guy on youtube with a 300hp 114i but again. No explaination on what he did to acheive those numbers.☹

 

I have a MHD stage 1 on my 2014 116i (136bhp).
MHD claim 'upto 200bhp' and it feels like it.
Their stage 2 will give more but needs a larger downpipe and intercooler for 235bhp.

MHD Super Tuning License for N13

The MHD Flasher F+G Series is a complete flash tuning app for your BMW. Unlike a piggyback module, it is capable of complete DME remapping while retaining all OEM safety mechanisms. This allows for maximum performance,maximum safety, and unrivaled drivability. You can install MHD right at home...

mhdtuning.com

You remap it yourself using the app and their wireless obd adaptor and can choose from some options.

I would start with the stage 1 maps first and then upgrage to a stage 2 once you have done the mods.

You buy the adaptor, the licence and whichever map pack you want. You need to use a battery stabiliser such as a large battery charger (20-30amp) or perhaps jump leads from a second fuly charged battery.

Its £193 for licence and £52 for stage 1 or 2 map pack + £70 for the wifi adaptor from

MHD Universal WiFi OBDII Flash Adapter

It’s the ultimate wireless connection method for tuning and coding your BMW & Supra MK5 with the market leading mobile apps!

www.mlperformance.co.uk

I strongly recommend you use the MHD if you are confident about doing it yourself, or a BMW tuning specialist. DO NOT use general a remapping company as the N13 engine is easy to wreck very quickly if the AFR, boost and timing is out.

 

have a look at bootmod3 license,pretty much the same as mhd except boost levels etc,and bm3 has more options

 

Before I installed the MHD, I checked the boost, it was barely getting to 10psi, which is okay for 136bhp.

After the remap, it peaked at 17.

MHD released a map update in the spring for "better boost profile" and afterwards I noticed they'd reduced the boost to 16psi but I didn't feel any effect on the performance.