Recently there has been an invention that allows you to send messages to the future! Hi future! In order to transport these messages, there are many different paths you can choose. These paths are arranged on a $4$ dimensional grid, where the past is at $(0,0,0,0)$ and the future is at $(8,8,8,8)$. However, the path cannot simply be traversed; it must form the shape of a tetrahedron! How many possible paths exist such that the vertices of this tetrahedron are on integer coordinates?