Generate a list without accepting some values

I want to create a random list of tuples where each tuple is the same length (say 6 for example) and is made up of a random selection of values = [0, 15, 30, 45, 60].

An example solution would be [(0, 30, 60, 0 , 15, 0)...(15, 45, 45, 0, 30, 60)]. However, I don't want to accept (0, 0, 0, 0, 0, 0) as a solution.