  In this note, we prove that for every ordinary genus-2 curve $X$ over a
finite field $\kappa$ of characteristic 2 with
$\text{Aut}(X/\kappa)=\db{Z}/2\db{Z} \times S_3$, there exist
$\text{SL}(2,\kappa\sembrack{s})$-representations of $\pi_1(X)$ such that the
image of $\pi_1(\bar{X})$ is infinite. This result gives a geometric
interpretation of Laszlo's counterexample [12] to a question regarding the
finiteness of the geometric monodromy of representations of the fundamental
group [4].
