The rational homology of the outer automorphism group of $F_7$

We compute the homology groups $H_{\ast }(\mathrm{Out}(F_7);\mathbb{Q})$ of the outer automorphism group of the free group of rank $7$. We produce in this manner the first rational homology classes of $\mathrm{Out}(F_n)$ that are neither constant ($\ast =0$) nor Morita classes ($\ast =2n-4$).