Not sure about the coding, since I have not had to deal with that, but it’s not that hard to replace, you just have to remove the cowling beneath the windshield. Because it is enclosed, it is vented to the outside, so you need to get a battery that is compatible with that. Or do what I did, and find a place that is offering a special for free battery install with purchase and take full advantage of not doing it yourself! Ha ha.... then you just need to get it registered to the ECU. With that year, I’m almost positive that you have the IBS (intelligent battery system). Before I got mine registered, after it was replaced, the lights and gauges would not work properly, so I wouldn’t recommend ignoring this step. Like Minnie said above, you can pay a dealership or Indy shop to do this, I don’t know what they charge for it, or have someone with the right scan tool do it for you, or buy one for yourself. I used my Schwaben like Minnie states above. Works great, but unless you will be using it for other things as well, it’s a bit pricey at over $200. But well worth it if you are planning on turning your own wrenches on your Mini, since it has many functions.
Good luck. There’s no reason to pay full price at Mini for a battery. Most competent service writers will be able to look up the correct battery to fit your car. I was out the door with a new one installed for around $175 or so, you can find a decent deal if you shop around and ask people to price match.