A high-spin isomer with τ>700 ns has been found in Hg204, populated in reactions of 1360-MeV Pb208 and 330-MeV Ca48 beams with a thick U238 target and a 1450-MeV Pb208 beam on a thick Pb208 target. The observed γ-ray decay of the isomer has established the yrast states below it, including another isomer with τ=33(3) ns. The experimental results are compared with shell-model calculations that include four holes in the configuration space between Sn132 and Pb208. 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 τ>700 ns isomer is the 22+ state of maximum spin available from the alignment of the four valence holes with the configuration πh11/2-2νi13/2-2.