  A projective symplectic variety $\mathcal{P}$ of dimension 6, with only
finite quotient singularities, $\pi(\mathcal{P})=0$ and
$h^{(2,0)}(\mathcal{P}_{smooth})=1$, is described as a relative compactified
Prym variety of a family of genus 4 curves with involution. It is a Lagrangian
fibration associated to a K3 surface double cover of a generic cubic surface.
It has no symplectic desingularization.
