Well it appears that the Mugen-tuned Honda will be coming sooner than you think, officially released you will be able to enjoy the Mugen Civic RR sometime this year (roughly about September). Being modded from a Civic Type R a sweet weight loss is exactly what Mugen has given the RR. Designing it to be the ultimate front-engine/front -wheel-drive performance ca, the RR has loss a total 10kg in comparison to the Civic Type R's intial weight.
In addition to the weight loss, the Mugen RR picks up 15 horsepower over the regular Type R. It's rated at 240 horses at 8,000 rpm and 160 lb-ft at 7,000 rpm.

Complementing the added power and and decreased weight are a new bodykit, upgraded brakes all around, a retuned suspension, new wheels and tires, and logo-emblazoned Recaro sport buckets. Availability is limited to 300 cars, all in Milan Red , and the pricing in Japan has been set at ¥4,777,500 ($38,750 USD).

Mugen's official website has a video of the car lapping Japan's Tsukuba circuit in 1:06:68, check out the link to see it in action.

Source: MUGEN via Carview and Jalponik