There is a new Tech Service Bulletin (TSB 0107-14 ) that helps with diagnosing and repairing this condition on the 2012-2014 Corolla and the 2012-2013 Matrix with code P219A. Please follow the TSB instructions for a proper repair.
We usually see these with just misfire (P0301, P0302, P0303 and P0304) codes and if you look at the FF "Freeze Frame) data, it should show a Run Time of about 60 seconds and the IAT/Coolant Temps about the same temp.
The problem is that the exhaust valves are not seating properly and you can test this by flipping the head over and filling the head with water. You can apply air pressure or wait overnight and see if the water leaks out of the exhaust side.
We usually see these with just misfire (P0301, P0302, P0303 and P0304) codes and if you look at the FF "Freeze Frame) data, it should show a Run Time of about 60 seconds and the IAT/Coolant Temps about the same temp.
The problem is that the exhaust valves are not seating properly and you can test this by flipping the head over and filling the head with water. You can apply air pressure or wait overnight and see if the water leaks out of the exhaust side.