  We prove that every K3 surface with automorphism group
$(\mathbb{Z}/2\mathbb{Z})^2$ admits an explicit birational model as a double
sextic surface. This model is canonical for Picard number greater than 10. For
Picard number greater than 9, the K3 surfaces in question possess a second
birational model, in the form of a projective quartic hypersurface,
generalizing the Inose quartic.
