If you have cat codes, you likely have stuck injectors. On naturally aspirated vehicles, you can run bg 44k or similar pro cleaner thru the system to get them unstuck. Due to the pressures involved, you will want to try a GDI specific product, preferably at a shop, if you want to give it a go. They will have the induction cleaning systems to do it right. Valvoline service centers for example.
If you change 1, change them all.
Misfires can also be caused by a) carbon buildup on the backs of the intake valves, b) crud from intercooler buildup being pulled into the intake, and c) tho rare on gen v, chafing knock sensor wires.
get ALL the fluids up to date: coolant, trans, ptu, rdu, and brake. Check for pooling oil in the turbo piping. Check and clean out the intercooler. Make sure all recalls - such as fuel pump delivery/control modules - are done.
Use SN+ (or later) oils only. If you are in a hot climate, 10w30 may work better for you than 5w30. Redline LWSP for ptu/rdu fluids recommended, or Amsoil Severe Gear of appropriate viscosity. Motorcraft MERCON LV is fine for the trans, though i like Valvoline MAXLIFE MV better. Coolant can be flushed for YELLOW, or go to a universal like Peak 10x / prestone 300k. If your SHO is speced for LV brake fluid, OEM is fine.
The first major mod you make should always be to establish a strong foundation.