If it's JUST homebrew: Hope you have a N3DS XL and find a primary entry point or get someone else with homebrew to set you up a secondary entry point.
If it's CFW you're after, read this:
11.4 is going to require either a hardmod or a DSiWare Transfer. The first requires you spend some money on tools or a person to do it for you. Doing it yourself requires soldering skills. Having someone do it for you requires the shipping times and modding times where you will not have access to your system.
The DSiWare method may seem less expensive at first, but you have to have a second system that's already hacked and the cheapest option I've seen for that method is an MK7 2DS for about $70 (That's how I did this method for 11.1 before safehax/soundhax). So not only will it cost about the same as getting someone else to do a hardmod, but you gotta find the 2DS near you or get it shipped and then take the time to hack it, get the DSiWare ready, then perform a system transfer and use the DSiWare to hack the new 3ds.
So either way, you will be spending time and money. There is a 3rd option that is in development which will be cheaper, but not free and still requires you wait until the guys developing it deem it ready for public release. It will require an NDS flashcart (like an R4) which you can probably find for $15