Let $B_n$ denote the braid group with $n$ braids. The Burau representation $B_n\to GL_n(\mathbb{Z}[t^{\pm1}])$ makes $(\mathbb{Q}[t^{\pm1}])^n$ a $B_n$-module. I am curious in knowing what $H_i(B_n, (\mathbb{Q}[t^{\pm1}])^n)$ is for $1<i<n$. Any reference is appreciated. Thank you in advance.

P.S. A google search tells me that the homology of braid groups with coefficients in the determinant of the Burau representation is calculated in a paper of C. De Concini, C. Procesi, and M. Salvetti.