Sorry, I don't have a hard & fast answer. I've never coded it myself, but I've given it a bit of thought over the years.

Things to consider:

1. When creating a Tic-Tac-Toe system, my personal preference is to have a 2D game at 3x3, a 3D game at 4x4x4 and a 4D game at 5x5x5x5. This gets fun, because there is no center square in 3D, and 4D just gets wacky.
2. Think about "What is a win?" in terms of vectors, so that what you create is scalable.
3. You want to write your rules so that they can be rotated. If you're playing in 2D, the board can be rotated in one of 4 positions. Write the rule once, if you're checking against board state, and then rotate those states. In 3D, you'll have 6x4 rotations and in 4D you'll have 8x6x4, I think...