Dimethylates the guanine residues at position 26 and 27 of one or more tRNAs using S-adenosyl-L-methionine as donor of the methyl groups. guanosine(26)/guanosine(27) in tRNA + 4 S-adenosyl-L-methionine = 4 H(+) + N(2)-dimethylguanosine(26)/N(2)-dimethylguanosine(27) in tRNA + 4 S-adenosyl-L-homocysteine Belongs to the class I-like SAM-binding methyltransferase superfamily. Trm1 family.