Take N gates, normalize them, represent them as points on the surface of a hypersphere. Quantize the hypersphere as coarsely as you need to get the precision you want. Want less precision but your quantization is getting too coarse? Increase N.

Fast algebraic codes exist to convert positions on a hyperspheric-ish surfaces to indexes and vice versa.

Perhaps spherical VQ isn't ideal-- though I suspect it is, since groups of weights often act as rotations naturally-- but some other geometry should be good if not.