Wishart linear form

Suppose $X=(X_1,X_2,X_3,X_4{)}^T$ ~ $N_4(0,I_2$ ⊗ $\sum )$ with $\sum =[[2,-1],[-1,2]]$. Define $Z=[[X_1,X_2],[X_3,X_4]]$ and Q = ZᵀZ. If $W_m(n,\sum )$ denotes a Wishart distribution of order m with n degrees of freedom, the distribution of $Q_{11}+Q_{12}+Q_{21}+Q_{22}$ is