Testbeam experiment 576 (T576) at the SLAC National Accelerator Laboratory sought to make the first measurement of coherent radio reflections from the ionization produced in the wake of a high-energy particle shower. The >10 GeV electron beam at SLAC End Station A was directed into a large high-density polyethylene target to produce a shower analogous to that produced by an EeV neutrino interaction in ice. Continuous wave (CW) radio was transmitted into the target, and receiving antennas monitored for reflection of the transmitted signal from the ionization left in the wake of the shower. We detail the experiment and report on preliminary hints of a signal consistent with a radio reflection at a significance of 2.36$sigma$. We recommend another test-beam measurement in order to verify the signal.