A search for an exotic baryon resonance with $S=\ensuremath{-}2$, $Q=\ensuremath{-}2$ has been performed in quasireal photoproduction on a deuterium target through the decay channel ${\ensuremath{\Xi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\Lambda}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\rightarrow}p{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{\ensuremath{-}}$. No evidence for a previously reported ${\ensuremath{\Xi}}^{--}(1860)$ resonance is found in the ${\ensuremath{\Xi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{\ensuremath{-}}$ invariant mass spectrum. An upper limit for the photoproduction cross section of 2.1 nb is found at the 90% confidence level. The photoproduction cross section for the ${\ensuremath{\Xi}}^{0}(1530)$ is found to be between 9 and 24 nb.