Criss Cross

A $4 \times 4$ grid is filled with digits $d$ , $0 \leq d \leq 9$ .

It can be seen that in the grid $\begin{matrix} 6 & 3 & 3 & 0 \\ 5 & 0 & 4 & 3 \\ 0 & 7 & 1 & 4 \\ 1 & 2 & 4 & 5 \end{matrix}$ the sum of each row and each column has the value $12$ . Moreover the sum of each diagonal is also $12$ .

In how many ways can you fill a $4 \times 4$ grid with the digits $d$ , $0 \leq d \leq 9$ so that each row, each column, and both diagonals have the same sum?

Write-up coming later

The complete problem is available here. An approach, code, and answer will be added later.