>>16740168
There is no solution.
Consider the grid as a 4x4 chess board. Every time you move, you switch colour. As there are 15 squares to step in, there are 15 movements, and therefore 15 colour switches. This is an odd number, so the square colour must be inverted. However the bottom right square is the same colour as the top left square, so there is a contradiction. Therefore, it is impossible.