Time-expanded phase-sensitive optical time-domain reflectometry (TE-ΦOTDR) is a dual-comb-based distributed optical fiber sensing technique capable of providing centimeter scale resolution while maintaining a remarkably low (MHz) detection bandwidth. Random spectral phase coding of the dual combs involved in the fiber interrogation process has been proposed as a means of increasing the signal-to-noise ratio (SNR) of the sensor. In this Letter, we present a specific spectral phase coding methodology capable of further enlarging the SNR of TE-ΦOTDR. This approach is based on the use of a quadratic spectral phase to precisely control the peak power of the comb signals. As a result, an SNR improvement of up to 8 dB has been experimentally attained with respect to that based on the random phase coding previously reported.