Update: I think I actually found a 22-step solution for real this time. Disclaimer: I still don't know how to play Rubik's cube. But I realized a valid scramble can be composed of simpler valid scrambles, so I tried to construct simpler permutations that are valid (tested with online solver and reversed the solution to get the scramble sequence, I still can't solve anything) and composed them together that might get what is needed.
Its scramble sequence is R2 B2 L2 U R2 F2 D R2 U2 F' L U' B D' L R D R F' U R' U
It's basically a composition of 3 ideas (partly thanks to the comments of @AxiomaticSystem)
switch all diametrically opposite corners (keeping side colors on the opposite faces):
solve: U R L D2 R L' U2 F2 D2 F2 B2 L2 B2 D2 F2 U
cause: U' F2 D2 B2 L2 B2 F2 D2 F2 U2 L R' D2 L' R' U'
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flip colors on all edges' sides
solve: R L U2 F U' D F2 R2 B2 L U2 F' B' U R2 D F2 U R2 U
cause: U' R2 U' F2 D' R2 U' B F U2 L' B2 R2 F2 D' U F' U2 L' R'
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twist 4 upper corners clockwise, 4 lower corners counterclockwise (can't twist them in all the same direction)
solve: R2 B U2 F2 U R2 L2 F2 D2 F B2 U2 F2 U2 D F2 D2 L2
cause: L2 D2 F2 D' U2 F2 U2 B2 F' D2 F2 L2 R2 U' F2 U2 B' R2
And after composing these three scrambles, I found only a few squares on the sides are the same color so I just need to twist up once, then solve it and invert the sequence to get this scramble. I still don't know how to find a 14-step solution though, good luck to you all!
(the following is obsolete but kept here in case it's useful to anyone)
Update: this solution is wrong, online solver said it's "solved", didn't report an impossible scramble, but the final result is not solved, but has switched colors on the four corners on the white and yellow faces like this picture. I don't know how to fix it yet, maybe someone more familiar with Rubik's cubes can find a solution.
Disclaimer: I don't know how to play Rubik's cube. I just found a way to assign colors on faces and tested in an online solver, and it kept saying I need to twist a corner or something, so I twisted 2 corners (with trial and error) and found this solvable with 22 steps:
Details: I figured you need at least 5 colors on a face, for example like this:
A B C
C D E
E A B
And I thought I'd try to distribute each color on 5 faces, 1 with it on the center and 2 each on 4 other faces, heck, let's try it on 4 adjacent faces of the face with that color in the center. (At least I know you can't change the color of a face's center by twisting :) For consistency's sake, I first tried making the color on an edge the same as the center of the face adjacent to that edge, and the corresponding colored corner on the counterclockwise side of the opposite edge (as in the above grid). And the online solver said it's unsolvable, and a corner needs to be twisted. I tried twisting a corner counterclockwise(the only way to avoid repeated colors), and it still said I need to twist a corner. I tried a few other things and it said I need to add all corners once or all edges once or something, so I figured that must be worse, why not go back and twist another corner instead? I figured out twisting two adjacent corners won't work because that repeats colors, so I next twisted two corners that are diagonally opposite on the cube, and it worked. Edit: I made a mistake and thought twisting corners diagonally opposite on a face also seems to work, but it doesn't because it repeats a color.