We consider high-dimensional multiuser MIMO transmissions in Frequency Division Duplexing systems. For precoding, the frequency selective channel has to be measured, quantized and fed back to the base station by the users. In 5G New Radio (NR), a modular quantization approach has been applied for this, where first a low-dimensional subspace is identified for the whole frequency selective channel, and then subband channels are linearly mapped to this subspace and quantized. We analyze how the components in such a modular scheme contribute to the overall quantization distortion. Based on this analysis we improve the technology components in the modular approach. We compare the improved quantization scheme to the 5G NR standardized version by simulation in a scenario with a realistic spatial channel model. The improvements lead to a more than 25% improvement in spectral efficiency.