Let $X$ be a finite CW-complex of $n$. We can consider $\pi_i (X)$'s as $\mathbb{Z}\pi_1 (X)$-module ($i\geq 2$). Moreover, if $\tilde{X}$ is the universal covering of $X$, then $H_i (\tilde{X})$ is a finitely generated $\mathbb{Z}\pi_1 (X)$-module for $i\geq 2$.

My question: is that is there relation between $\pi_i (X)$'s as $\mathbb{Z}\pi_1 (X)$-module and $H_i (X)$'s as $\mathbb{Z}$-module or $H_i (\tilde{X})$ as $\mathbb{Z}\pi_1 (X)$-module for $2\leq i\leq n$?

I know that the connection between homotopy groups and homology groups is given by the Hurewicz-Theorem. But I want a relation between $\pi_i (X)$'s as $\mathbb{Z}\pi_1 (X)$-module and $H_i (X)$'s as $\mathbb{Z}$-module or $H_i (\tilde{X})$ as $\mathbb{Z}\pi_1 (X)$-module particularly when they are free for $2\leq i\leq n$.