A search for dark matter axions with masses \(>10 \mu eV/c^{2}\) has been performed using the HAYSTAC experiment's squeezed state receiver to achieve sub-quantum limited noise. This report includes details of the design and operation of the experiment previously used to search for axions in the mass ranges \(16.96-17.12\) and \(17.14-17.28 \mu eV/c^{2}\)(\(4.100-4.140\)GHz) and \(4.145-4.178\)GHz) as well as upgrades to facilitate an extended search at higher masses. These upgrades include improvements to the data acquisition routine which have reduced the effective dead time by a factor of 5, allowing for the new region to be scanned \(\sim\)1.6 times faster with comparable sensitivity. No statistically significant evidence of an axion signal is found in the range \(18.44-18.71\mu eV/c^{2}\)(\(4.459-4.523\)GHz), leading to an aggregate upper limit exclusion at the \(90\%\) level on the axion-photon coupling of \(2.06\times g_{\gamma}^{KSVZ}\).