  In this work, subcovers $\mathcal{X}_{n,r}^s$ of the curve
$\mathcal{X}_{n,r}$ are constructed, the Weierstrass semigroup $H(P_\infty)$ at
the point $P_\infty \in \mathcal{X}_{n,r}^s$ is determined and the
corresponding one-point AG codes are investigated. Codes establishing new
records on the parameters with respect to the previously known ones are
discovered, and $108$ improvements on MinT tables are obtained.
