Hi, welcome to TA. Upload some pictures man, we always like to see Type R's here
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You're not the first person to sign up asking how to take their Accord to 250BHP. The thing you've got to consider is that your engine is Naturally aspirated, so to see a 38HP gain is going to require some serious spending £££. Consider a complete replacement (sports upgrade) of air intake, inlet and outlet manifold and exhaust (including sports cat). That will get the car pushing out more, but it still won't yield the kind of increases you're looking for. After that, it's really just upgrading some internals of the engine. Again, very costly :unsure: . I don't know what/if there are any options for a more aggressive ECU remap to compliment the above mentioned upgrades, but if there are, that would certainly improve things. Hondata is the company you need to look at for that. One of our admins here (F6had) has a tuning company with a great reputation. He does a lot of work for people here. I don't know if he offers anything for the 6th Gen Type R, but it's worth enquiring.
Have you been out and ragged it a bit to get a feel for it yet? The Type R is an animal and has a great chassis and with the limited slip diff, if handles brilliantly. If I were you, I'd look into coil over suspension and chassis stiffening rather than engine performance. The Type R is indicative of Honda's ethos of handling sophistication over brute power. I.e. it may get beaten in the straights, but it owns much higher spec cars through the bends. Play to that, work to its strengths, don't get hung up on chasing Dyno figures and it will be an animal on the road and the track.
Of course, if you are dead set on seeing large gains, I think there are some options regards supercharging
. That would instantly push you into the high 200s possibly even low 300s. But again, it's costly and you may want to consider other engine mods to support it. With a jump in power like that, you might need to strengthen other aspects of the setup so that the engine doesn't go pop. All very expensive stuff.
Anyway, have a nose around the sight, make yourself at home, see what the other Type R owners here have to say on the matter. Oh, and if you want to search anything, use the custom Google search. The standard forum search is buggy and doesn't work properly.