Recent advances in Brillouin optical time-domain reflectometry (BOTDR) technology have enabled the high resolution distributed fiber optic sensing of strain and temperature. However, a high spatial resolution BOTDR, such as a synthetic BOTDR (S-BOTDR), has a weak point: the spectrum's signal-to-noise (SNR) is lower than conventional BOTDRs. To overcome this weak point, we propose a coded S-BOTDR using a Golay code sequence. The coded S-BOTDR's spectrum agrees with that of S-BOTDR on average; hence the high spatial resolution feature of S-BOTDR is preserved. We show that the spectrum's SNR increased and that the number of repetitions can be reduced by a coded S-BOTDR, although a limit exists that cannot be exceeded by increasing the code length.