No I don’t, I just made a wild guess. Good work going through fifty tries. I place my next guess on gods number being either 11 or 12. We’ll see though, I don’t have any proof.It is by no means short, but I did find this one a little while back.
[2R2 B2 D2 U2 F2 2R2 D2 F2 2L U2 2R2 F2 2L' U2 2R U2 2R', U2 B2 2R' B2 U2 2R U2 2R' B2 2R2 B2 U2 2R2] 2R
I was just searching using Cube Explorer (manually). I know the question was just to solve the first face, not necessarily the first layer. But even with solving the entire face, I couldn't find a position (with about 50 tries) which required more than 11. You mentioned 13 moves. Do you know of a position which requires 12 or 13?