  We consider the class of singular double coverings $X \to \PP^3$ ramified in
the degeneration locus $D$ of a family of 2-dimensional quadrics. These are
precisely the quartic double solids constructed by Artin and Mumford as
examples of unirational but nonrational conic bundles. With such quartic
surface $D$ one can associate an Enriques surface $S$ which is the factor of
the blowup of $D$ by a natural involution acting without fixed points (such
Enriques surfaces are known as nodal Enriques surfaces or Reye congruences). We
show that the nontrivial part of the derived category of coherent sheaves on
this Enriques surface $S$ is equivalent to the nontrivial part of the derived
category of a minimal resolution of singularities of $X$.
