This study investigates covert communication in multi-sensor systems employing Intelligent Reflecting Surfaces (IRSs). Different from previous works, we focus on optimizing transmission amplitudes and phase angles for a 2-BPSK codebook in the presence of asymmetric noise over complex Gaussian channels. We adopt KL divergence as a covertness constraint and mutual information as a metric for transmission rate. We employ Taylor series expansion to approximate KL divergence and mutual information. Leveraging these approximations, we derive optimal phase angles through a proposed gradient descent algorithm. The numerical simulations validate the effectiveness and precision of our Taylor approximation method. Through validation in different scenarios, our algorithm demonstrates robust convergence, deriving all optimal phase angles. Comparing initial phase angles from prior works to those obtained via our algorithm, we observe a higher covert transmission rate.