Optophononic resonators based on GaAs/AlAs multilayer structures can confine near-infrared photons and subterahertz phonons. Previous works have studied the generation and detection of coherent acoustic phonons in planar and circular micropillar cavities. However, these structures exhibit only one optical cavity mode, which makes it challenging to reach the efficient generation and sensitive detection simultaneously in a standard pumpprobe experiment. Here, we propose the use of elliptical micropillars to reach an improved condition of these two processes. The elliptical cross-section of the microcavity lifts the degeneracy of the fundamental optical modes, related to each of its major and minor axes. By tuning the pump pulses in resonance with one optical mode, the generation efficiency is enhanced by maximizing the electromagnetic field inside the cavity. Meanwhile, the probe pulses at the same wavelength and with orthogonal polarization detects phonons at the slope of the other mode, where it is sensitive to reflectivity changes. We experimentally demonstrated that the phonon amplitude is enhanced by introducing the ellipticity compared to the circular micropillar. This improvement is promising for future developments in constructing efficient phonon transducers.