We craft a special class of unitary matrices over $\mathbb{F}_{q^2}$ to generate classical linear codes whose Hermitian hulls have dimensions that we can design. We then use the codes as classical ingredients in the construction of good entanglement-assisted quantum codes. Over finite fields of characteristic $2$, we propose two explicit constructions. To highlight their efficacy, we list excellent qubit codes whose parameters are either new or strictly better than comparable best-known codes in the literature.