A high-spin isomer with $\ensuremath{\tau}g700$ ns has been found in $^{204}\mathrm{Hg}$, populated in reactions of 1360-MeV $^{208}\mathrm{Pb}$ and 330-MeV $^{48}\mathrm{Ca}$ beams with a thick $^{238}\mathrm{U}$ target and a 1450-MeV $^{208}\mathrm{Pb}$ beam on a thick $^{208}\mathrm{Pb}$ target. The observed $\ensuremath{\gamma}$-ray decay of the isomer has established the yrast states below it, including another isomer with $\ensuremath{\tau}=33(3)$ ns. The experimental results are compared with shell-model calculations that include four holes in the configuration space between $^{132}\mathrm{Sn}$ and $^{208}\mathrm{Pb}$. The available spectroscopic information, including transition strengths, total conversion, and angular correlation coefficients, together with the observed agreement with the calculations, allows spin, parity, and configuration assignments to be proposed for the experimental states. The $\ensuremath{\tau}g700$ ns isomer is the ${22}^{+}$ state of maximum spin available from the alignment of the four valence holes with the configuration $\ensuremath{\pi}{h}_{11/2}^{\ensuremath{-}2}\ensuremath{\nu}{i}_{13/2}^{\ensuremath{-}2}$.