2003 Audi A4 it begins to output blue - black smoke

This smoke will be oil smoke, I would do an oil consumption test first, change oil and filter make sure oil is exactly on full mark, note mileage and run for one week and check oil, if low add but measure amount used and note mileage. Report back findings, check sparks plug for contamination (oil fouling) is there any smoke (blue) when starting up cold? If not there may be an oil control issue happening, or a turbo oil seal. If a turbo seal is faulty you will see small specks of oil on the back of the car and the tail pipe will be greasy with a little oil as a turbo oil seal leak will not fully burn the oil entering the exhaust.