We present a hardware realization and measurements of a tetron qubit device in a superconductor-semiconductor heterostructure. The device architecture contains two parallel superconducting nanowires, which support four Majorana zero modes (MZMs) when tuned into the topological phase, and a trivial superconducting backbone. Two distinct readout interferometers are formed by connecting the superconducting structure to a series of quantum dots. We perform single-shot interferometric measurements of the fermion parity for the two loops, designed to implement Pauli-$X$ and $Z$ measurements of the tetron. Performing repeated single-shot measurements yields two widely separated time scales $\tauX = \SI{14.5\pm 0.3}{\micro\second}$ and $\tauZ = \SI{12.4\pm 0.4}{\milli\second}$ for parity switches observed in the $X$ and $Z$ measurement loops, which we attribute to intra-wire parity switches and external quasiparticle poisoning, respectively. We estimate assignment errors of $\errXa = 16\%$ and $\errZa = 0.5\%$ for $X$ and $Z$ measurement-based operations, respectively.