Hyundai i30: engine problems

We purchased a new Hyundai i30 in September and have experienced an intermittent problem ever since. It occurs when starting the car, when for 20-30 seconds it runs extremely rich, to the point that black smoke billows from the exhaust and the engine is only running on two or three cylinders. The dealer has been unable to find the fault, despite changing the injectors and fitting the car with a recording device to catch it. The dealer has now told me told that the problem needs to be sorted by Hyundai, but Hyundai Customer Service said the dealer needed to sort it out. Whilst I understand intermittent problems are hard to fix I can't see how any progress can be made without somebody inspecting the car and at least attempting to do something. We would appreciate any help you can give in this matter.