Today I got the complete VFD tube setup working. Some parts still get a bit hot so the system switches off after 15 minutes but I think with some heat transfer paste and better heat sinks I can get rid of this problem.
As you can see in the video below the tubes need a supply voltage of 25 V. This voltage is converted to 1 V and 5 V for the microcontroller. Lets hope I have a nice clock soon ;). Please read this article for further information.