  Given an integer $\gamma\geq 2$ and an odd prime power $q$ we show that for
every large genus $g$ there exists a non-singular 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 possible. This answers a recent conjecture by Faber--Grantham.
Our methods are based on curves on toric surfaces and Poonen's work on
squarefree values of polynomials.
