S-adenosyl-L-methionine-dependent methyltransferase that acts as a component of the wybutosine biosynthesis pathway. Wybutosine is a hyper modified guanosine with a tricyclic base found at the 3'-position adjacent to the anticodon of eukaryotic phenylalanine tRNA. Probably methylates N-4 position of wybutosine-86 to produce wybutosine-72. 4-demethyl-7-[(3S)-3-amino-3-carboxypropyl]wyosine(37) in tRNA(Phe) + S-adenosyl-L-methionine = 7-[(3S)-3-amino-3-carboxypropyl]wyosine(37) in tRNA(Phe) + H(+) + S-adenosyl-L-homocysteine tRNA modification; wybutosine-tRNA(Phe) biosynthesis. Present with 3390 molecules/cell in log phase SD medium. Belongs to the TYW3 family.