Snake game on a 9×9 grid

You are playing a snake game. The snake starts in the top-left corner of a grid. Each cell of the grid is either empty or a wall. Each turn you can press a key to move the snake in one of four directions: either horizontally or vertically. Once a key is pressed, the snake moves in the assigned direction until it either reaches a wall or the boundary of the grid. Can you construct a $9 times 9$ grid with $4$ walls such that the snake is able to visit every empty cell of the grid?

Here is a simpler version of this puzzle: Snake game on a 6×6 grid