  Balanced weighing matrices with parameters $$
\left(1+18\cdot\frac{9^{m+1}-1}{8},9^{m+1},4\cdot 9^m\right), $$ for each
nonzero integer $m$ is constructed. This is the first infinite class not
belonging to those with classical parameters. It is shown that any balanced
weighing matrix is equivalent to a five-class association scheme.
