From current description:

You can only travel through doors if you have the correct key. However, you can travel over the exit even if you don't have all the keys

The grid below has solution, but I'm getting that grid has no solution
.#a.C..
.####..
b#.@...
B#...##
.#c.#$.
....A..

Your solution was: [(3, 2), (3, 3), (3, 4), (2, 4), (2, 3), (2, 2), (3, 2), (4, 2), (5, 2), (5, 1), (5, 0), (4, 0), (3, 0), (2, 0), (3, 0), (4, 0), (5, 0), (5, 1), (5, 2), (4, 2), (4, 3), (3, 3), (3, 4), (3, 5), (4, 5), (5, 5), (5, 4)]
However, the grid was unsolvable.

And it has solution as there is way to get the key 'c' after that unlock door C, pickup key 'a', then unlock key A and then exit door