  For all integers $g \geq 6$ we prove the existence of a metric graph $G$ with
$w^1_4=1$ such that $G$ has Clifford index 2 and there is no tropical
modification $G'$ of $G$ such that there exists a finite harmonic morphism of
degree 2 from $G'$ to a metric graph of genus 1. Those examples show that
dimension theorems on the space classifying special linear systems for curves
do not all of them have immediate translation to the theory of divisors on
metric graphs.
