Efficient channel state information (CSI) compression at the user equipment plays a key role in enabling accurate channel reconstruction and precoder design in massive multiple-input multiple-output systems. A key challenge lies in balancing the CSI feedback overhead with the achievable downlink rate, i.e., maximizing the utility of limited feedback to maintain high system performance. In this work, we propose a precoding-oriented CSI feedback framework based on a vector quantized variational autoencoder, augmented with an information-theoretic regularization. To achieve this, we introduce a differentiable mutual information lower-bound estimator as a training regularizer to promote effective utilization of the learned codebook under a fixed feedback budget. Numerical results demonstrate that the proposed method achieves rates comparable to variable-length neural compression schemes, while operating with fixed-length feedback. Furthermore, the learned codewords exhibit significantly more uniform usage and capture interpretable structures that are strongly correlated with the underlying channel state information.