Do a search on Castboolits for the old group buy for a 225107 mold by NOE (Night Owl Enterprises). Or check their website.
If that bullet shape suits you, contact them and see if they will run a custom oversize mold for you, likely as a plain base. They had ran some oversize to suit the Savage .22 High Power reloaders, at .228". It's a pretty straightforward programming change, the hard part is getting it slid in to the schedule.
Other wise, it's a search for suitable mold, as well as for someone to open it up enough to suit your bore. The molds with potential to be suitable would likely be the .225438, the 225107, and the 225415 though that last may be a bit heavy. The 225438 is still made, as is the 225415. They would all need to be opened up for your purposes.
Then you will also probably want a custom sizing die too (easy, open up a .224" or .225" one).
This, all in addition to having to learn how to cast a good, small bullet. Fun!
edit: Another avenue worth a look might be to learn about paper patching, and wrap some available .225 size cast bullets up to the size you need, or have a swage die built to swage your own lead slugs that could be paper patched. The forces for swaging a lead slug of this size are well withing the reach of most reloading presses, and if paper patching, you do not need lube grooves etc. It would be a little fiddly to learn on the small slugs, but do-able.
The bullet can be as simple as a straight sided, flat on both ends, slug.
Cheers
Trev