  Sarvepalli and Klappenecker showed how classical one-point codes on the
Hermitian curve can be used to construct quantum codes. Homma and Kim
determined the parameters of a larger family of codes, the two-point codes. In
quantum error-correction, the observed presence of asymmetry in some quantum
channels led to the study of asymmetric quantum codes (AQECCs) where we no
longer assume that the different types of errors are equiprobable. This paper
considers quantum codes constructed from the two-point codes. In the asymmetric
case, we show strict improvements over all possible finite fields for a range
of designed distances. We produce large dimension pure AQECC and small
dimension impure AQECC that have better parameters than AQECC from one-point
codes. Numerical results for the Hermitian curves over F16 and F64 are used to
illustrate the gain.
