As far as speed ratings, GTI's in Europe come with W rated tires and mostly with Michelin, Bridgestone, Continental and Pirelli. Exception was the ED30 which came with Z-Y rated tires.
As far as top speed, in Europe most electronically limited cars are set to 250kph/155mph. Officially, Volkswagen has announced 235kph/146mph for GTI's top speed but I have a feeling that this is also electronically limited, it seems too low to be the car's actual top speed. For ED30 they had announced 245kph/153mph but I know for a fact that this was indeed electronically limited, because I have seen a stage 2+ ED30 (~360bhp on stock K04) hitting 280kph/174mph.
Now to the OP's question in specific...
Oettinger offers a GTI project with 330bhp and 450nm with a top speed of 270kph/168mph. That car is equipped with a rather expensive list (copied from Oettinger website):
* OETTINGER turbocharger
* Recalibration of the engine management - via Directport
* OETTINGER motorsport catalytic converter
* OETTINGER front- and main silencer
* OETTINGER rear silencer
* OETTINGER injector valve
* OETTINGER intercooler - enlarged
* OETTINGER high pressure fuel pump
I don't know if the Oettinger turbo is like a K04 in size, or bigger. Judging from both horsepower and torque my guess goes to K04. The other parts look more or less like a stage 2+. So, this is your answer for a (probably) K04 project. Their other projects have a much lower top speed, 255kph/159mph and down.