A random access distributed Brillouin fibre sensor is presented, based on phase modulation using a pseudo-random bit sequence (PRBS) together with time gating. The standard phase-correlation technique is known to show a noise level increasing linearly with the number of measured points due to weak gratings generated randomly along the whole sensing fibre. Here we show how intensity modulated pump and time gated detection significantly improve the signal-to-noise ratio (SNR) of the system with no impact on the spatial resolution. A measurement with 1.1 cm spatial resolution over 3.3 km is demonstrated, representing 300’000 equivalent points. The limitations of the proposed technique are discussed through the paper.