Long-range Rayleigh-based Distributed Acoustic Sensing (DAS) systems are often limited in their sensitivity and bandwidth. The former limitation is a result of the low backscattered power and poor \textit{dynamic-strain to optical-phase} transduction efficiency. The latter constraint results from the trade-off between range and scan-rate which limits the sampling interval to the longest delay in the sensing fiber. Quasi-DAS (Q-DAS) can yield enhanced sensitivity but may still suffer from low backscattered power and low scan-rate for long-haul, many-sensor, systems. In this work we study the use of Perfect Periodic Correlation codes for interrogating a long-haul Q-DAS system. It is shown that judicious choice of the code parameters allows order of magnitude increase in detection bandwidths and in the power reflected from each sensor.