  The spectrum of the glueball with $J^{PC}=0^{--}$ is computed using different
bottom-up holographic models of QCD. The results indicate a lowest-lying state
lighter than in the determination by other methods, with mass $m \simeq 2.8$
GeV. The in-medium properties of this gluonium are investigated, and stability
against thermal and density effects is compared to other hadronic systems.
Production and decay modes are identified, useful for searching the
$J^{PC}=0^{--}$ glueball.
