Beta-1,3-galactosyltransferase that transfers galactose from UDP-galactose to substrates with a terminal beta-N-acetylglucosamine (beta-GlcNAc) residue. Involved in the biosynthesis of N-glycans containing Lewis a structures (with the combination of FUT13). Protein modification; protein glycosylation. Interacts with GMII. Expressed in stems and siliques. Belongs to the glycosyltransferase 31 family.