  Given a gonality $\gamma$ and a prime power $q\geq \gamma -1$ we show that
for every large genus $g$ there exists a curve $C$ defined over $\mathbb{F}_q$
of genus $g$ and gonality $\gamma$ and with exactly $\gamma(q+1)$
$\mathbb{F}_q$-rational points. This is the maximal number of rational points
allowed. This answers a recent conjecture by Faber--Grantham. Our methods are
based on Poonen's work on squarefree values of polynomials together with a
Newton polygon argument.
