Jetta 2004 Black smoke when starting

Greetings:
I have a jetta that, when the Auto Auto Avies Black and Battle is starting to light by scanning it, I showed the following P1296, P1602 and P0420 codes.
The P1602 code I do not know if it marks it since we just changed the battery.
Which code do you think this causing the problem? Or what other problem do you think you have?

Thank you

The P1296 code refers to the cooling system, if it costs to start it and also pulls black smoke, I tilted with the coolant temperature sensor, the P0420 code refers to the catalyst if it is not or is covered, it causes a failure in the reading of the oxygen sensor, but the sensor is the sensor and it accuses it as a catalyst and vice versa, both affect in the time of the injector. There is black smoke for a fuel ex -stand.

OK thanks