  In this work we present a way to construct the so-called root diagram for
one-point AG codes $C$ arising from certain types of curves $\mathcal{X}$ over
$\mathbb{F}_q$ with plane model $f(y)=g(x)$. Using this root diagram we can get
an algorithm to obtain a Gr\"obner basis for the submodule $\overline{C}$
associated to $C$
