Variance of a Wishart quadratic form

Let $X_1, X_2, \dots, X_5$ be i.i.d. random vectors following the bivariate normal distribution with zero mean vector and identity covariance matrix. Define $5 \times 2$ matrix $X$ as $X = (X_1, X_2, \dots, X_5)^T$. Further, let $W = (W_{ij}) = X^T X$, and $Z = W_{11} + 4W_{12} + 4W_{22}$. Then $\operatorname{Var}(Z)$ equals