Polylycylase which modifies alpha- and beta-tubulin, generating side chains of glycine on the gamma-carboxyl groups of specific glutamate residues within the C-terminal tail of alpha- and beta-tubulin. Involved both in the side-chain initiation and elongation steps of the polyglycylation reaction by adding a single glycine chain to generate monoglycine side chains and by elongating monoglycine side chains to polyglycine side chains.