What is the genus of the complete $4-$partite graph $K_{4,2,2,2}$?

What i know: Since $K_{4,4,2}$ is a subgraph of $K_{4,2,2,2}$, and genus of $K_{4,4,2}$ is 2, $K_{4,2,2,2}$ has genus greater than or equal to 2. Also $K_{4,2,2,2}$ is a subgraph of $K_{10}$, so it genus is less than or equal to 4. My conjecture is that it is 2, so i try to embed on double torus, but i failed.

I have tried to find the genus even by using sage. But my computer is slow. Any one could help me to find the genus using sage programming. One could find the genus using the following program.

sage: g = Graph([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)])

sage: g.genus()

Thanks in advance.