The current best solution is 38 moves, found by Dr. Sonny Brooks:
      L1 D2 R6 U2 L5 U1 L1 D3 R5 U2 L4 D3 R3

Cihan Altay found this 39-move solution:
      D L D R5 U2 L6 R U L D3 R5 U2 L4 D3 R3

If you find a better solution, email me and I'll post it here with your name.

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