A new, hybrid time-domain and correlation-domain Brillouin analysis technique is proposed and demonstrated, providing a large number of high-resolution acquisition points. The method is based on dual-layer hierarchal encoding of both amplitude and phase. The pump and signal waves are co-modulated by a relatively short, high-rate binary phase sequence. The phase modulation introduces Brillouin interactions in a large number of discrete and localized correlation peaks along the fiber under test. In addition, the pump wave is also amplitude-modulated by a slower, carefully synthesized, long on-off-keying sequence. Brillouin interactions at the correlation peaks imprint weak replicas of the pump amplitude sequence on the intensity of the output signal wave. The Brillouin amplifications at individual correlation peaks are resolved by radar-like, matched-filter processing of the output signal, following a recently-proposed incoherent compression protocol. The method provides two significant advantages with respect to previous, pulse-gated correlation-domain analysis schemes, which involved a single pump pulse. First, compression of the extended pulse sequence enhances the measurement signal-to-noise ratio, which is equivalent to that of a large number of averages over repeating single-pulse acquisitions. The acquisition times are potentially much reduced, and the number of resolution points that may be practically interrogated increases accordingly. Second, the peak power level of the pump pulses may be lowered. Hence, the onset of phase pattern distortion due to self-phase modulation is deferred, and the measurement range can be increased. Using the proposed method, the acquisition of Brillouin gain spectra over a 2.2 km-long fiber with a spatial resolution of 2 cm is demonstrated experimentally. The entire set of 110,000 resolution points is interrogated using only 499 position scans per choice of frequency offset between pump and signal. A 5 cm-long hot-spot, located towards the output end of the pump wave, is properly recognized in the measurements.