Microwave cavities have been deployed to search for bosonic dark matter candidates with masses of a few μeV. However, the sensitivity of these cavity detectors is limited by their volume, and the traditionally employed half-wavelength cavities suffer from a significant volume reduction at higher masses. Axion dark matter experiment (ADMX)-Orpheus mitigates this issue by operating a tunable, dielectrically loaded cavity at a higher-order mode, which allows the detection volume to remain large. The ADMX-Orpheus inaugural run excludes dark photon dark matter with kinetic mixing angle χ>10^{-13} between 65.5 μeV (15.8 GHz) and 69.3 μeV (16.8 GHz), marking the highest-frequency tunable microwave cavity dark matter search to date.