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{F B'} D' L R D2 R' U2 R D2 R' U2 B L' U' D2 B R2 B2 L' F' L2 F L' F' U L' U' L F' L2 (31, 40, 30, 39)
Explanation : I played a while with the connected pair after F, and it turned out that I found this 11 moves 2x2x3 : {F B'} D' L B L' U' D2 B R2 B2. Then I tried U'F'U, which orients all edges and gives a 2x2x1 for free, but did not found anything after that. So I went for other CE pairs and postponed the orientation of the two edges : L'F'L2FL'F'(UL'U')LF'L2 after the 2x2x3 (UL'U' is the edges orientation.
So ...
FB'D'L.BL'U'D2BR2B2
L'F'L2FL'F'(UL'U')LF'L2 leaves 3 corners in 23 HTM, and the only insertion I found was (RD2R'U2RD2R'U2) at the dot, resulting in a quite ugly solution QTM-wise ...
Any ideas ?