  We give estimates of the Gromov norm of the top dimensional class in
$H_c^4(\mathrm{Isom}(\mathbb{H}_{\mathbb{C}}^2);\mathbb{R})$. As a consequence,
we obtain an explicit upper bound for the simplicial volume of closed oriented
manifolds that are locally isometric to $\mathbb{H}_{\mathbb{C}}^2$.
