Clarification needed first:
You say it's a 6 dice code, but list a 7 dice code. Which is it?
My mistake, it is a 6-dice code. I have edited the OP.
Does each die have the same symbol repeated, or does the repeated symbol change across the dice?
Each die is exactly the same.
How is the 6-dice code generated, is it using cards with a particular distribution etc? It matters because if the repeated symbol is always used twice etc, it will affect the probabilities.
There are only 8 cards (2 on display at a time). The designer appears to have chosen a the 8 combinations at random.