We study the problem of quantizing an M dimensional beamforming vector with M relatively large. Using a conventional beamforming vector codebook to quantize beamforming vectors incurs a complexity that scales exponentially with M, making it unsuitable when M is large. In, we proposed to use a trellis-based quantization scheme to tackle the complexity problem, and we present two enhancements in this paper. First, we let each trellis stage process multiple channel dimensions, resulting in a quantization improvement at the cost of increasing the quantization complexity to O(M22BL). Second, we permute the trellis state transitions and outputs to map neighboring beamforming vectors to neighboring channel coded vectors. The second enhancement is beneficial when implementing feedback, as feedback information is time-sensitive and retransmission may not be worthwhile. Simulations show the improvements of our proposed techniques.