Quantum random access codes (QRACs) constitute a fundamental framework for demonstrating the advantages of quantum resources and protocols, with wide-ranging applications in quantum information processing. In this work, we investigate the influence of parity-time ($𝒫𝒯$) symmetric non-Hermitian operations on noisy QRACs using an analytically tractable two-level model. Focusing on the $2^{(2)}\to 1$ QRAC, we show that non-Hermitian operations can enhance the dimension witness and restore quantum advantage in the presence of amplitude-damping, phase-damping, and phase-flip noise channels with appropriate parameters. We further analyze the limiting behavior of the model. Our results provide a proof-of-principle demonstration that suitably chosen non-Hermitian operations can improve the noise robustness of the $2^{(2)}\to 1$ QRACs.