We report an amplitude-measuring Rayleigh-based sensor that uses a series of frequency-shifted pulses to extract quantitative distributed strain measurements. By using frequency multiplexing, we are able to inject a train of 10 pulses into the fiber at once. This allows us to use a higher average input power than standard phase-sensitive optical time domain reflectometry systems, improving the sensitivity. The sensor recovers the strain by tracking the time-dependent amplitude of the Rayleigh backscattered light from all 10 pulses. This approach enables a sensor with a noise floor of 1.5pε/√Hz over 10 km of fiber with 12 m spatial resolution, a 5 kHz bandwidth, and a dynamic range of 80 dB at 1 kHz. The sensor exhibits a high degree of linearity and is immune to interference fading.