When starting from cold i get smoke and vibration. Ran VAG com and got

17664 Engine coolant temp sensor G62 open to short or + P1256/35-10 Intermitent

and

17672 PD Unit Injector Cylinder 2 (N242-Reg range Exceeded) P1264-35-10 Intermitent

Can anyone shed light as to what might be wrong. The injector code sounds like the issue. Is it an injector change ??

2002 A4 1.9Tdi 130 Sport.

Thanks