Welcome to the Phaeton forum, we're glad you are here.
I also own a 2004 W12 Phaeton. The owner manual for my car specifies 'G12' coolant, as shown in the scanned image below. To the best of my knowledge, this means you use the coolant shown in the picture below that. The text in the owner manual is a bit ambiguous - although it suggests that the 'purple coloured' G12 is desirable, it also states very clearly that we can use 'red' G12, or even G11. The liquid in the jug shown in the picture below is sort of a bright fluorescent red colour. I asked the Phaeton technician at my VW dealership about this, and he told me that it was 'for sure' perfectly OK to use the stuff shown in the picture. By the way, he also drives a Phaeton, and I trust his judgement absolutely.
You may also want to have a peek at these past discussions about coolant:
Some other great resources for you as a new Phaeton owner include our Phaeton Forum 'Table of Contents' (FAQ by Category) - especially the section entitled 'Questions New Phaeton Owners Have Asked', and the excellent team of support specialists available to you at the Phaeton Customer Care Center, who can be reached toll free by dialling 1 (877) 742-3866.
Best regards, happy motoring,