  We introduce a new class of evaluation linear codes by evaluating polynomials
at the roots of a suitable trace function. We give conditions for
self-orthogonality of these codes and their subfield-subcodes with respect to
the Hermitian inner product. They allow us to construct stabilizer quantum
codes over several finite fields which substantially improve the codes in the
literature and that are records at [http://www.codetables.de] for the binary
case. Moreover, we obtain several classical linear codes over the field
$\mathbb{F}_4$ which are records at [http://www.codetables.de].
