Involved in the galactan polymerization of the arabinogalactan (AG) region of the mycolylarabinogalactan-peptidoglycan (mAGP) complex, an essential component of the mycobacteria cell wall. Thus, successively transfers approximately 28 galactofuranosyl (Galf) residues from UDP-galactofuranose (UDP-Galf) onto the galactofuranosyl-galactofuranosyl-rhamnosyl-GlcNAc-diphospho-decaprenol (Galf-Galf-Rha-GlcNAc-PP-C50) acceptor produced by GlfT1, with alternating 1->5 and 1->6 links, forming a galactan domain with approximately 30 galactofuranosyl residues. beta-D-galactofuranosyl-(1->5)-beta-D-galactofuranosyl-(1->4)-alpha-L-rhamnosyl-(1->3)-N-acetyl-alpha-D-glucosaminyl-diphospho-trans,octa-cis-decaprenol + 28 UDP-alpha-D-galactofuranose = [beta-D-galactofuranosyl-(1->5)-beta-D-galactofuranosyl-(1->6)]14-beta-D-galactofuranosyl-(1->5)-beta-D-galactofuranosyl-(1->4)-alpha-L-rhamnopyranosyl-(1->3)-N-acetyl-alpha-D-glucosaminyl-diphospho-trans,octa-cis-decaprenol + 28 H(+) + 28 UDP Cell wall biogenesis; cell wall polysaccharide biosynthesis. Homotetramer. Belongs to the glycosyltransferase 2 family.