It seems like you are trying to find
One such example that satisfies this is
As mentioned by armb in the comments, there is a good answer here discussing the maximum orders for an $n \times n \times n$ Rubiks cube.
Here are some notes on my own approach:
1. Prep work
I did a lot of prep work ahead of time so that the combinatorial engine could run as efficiently as possible.
For example, I took each word in my word list and shifted it in a circular fashion into all possible positions around the wheel. I stored these results in a lookup array for quick referencing ...