Bigger what housing? Compressor or exhaust?
You cant put T4 internals in the T3 housings.
It sounds like a EscCos T34 compressor side with a Sierra T3 exhaust side.
So not a T4, good for about 350-370bhp if the spec above, or 400 at a push (35psi style push) with the .63 EscCos exhaust side.
Its a T34 basically.
Show me a pic and ill tell you exactly what it is.