Sensitivity of a plasmonic detector is enhanced by integrating a broadband log-periodic antenna with a two-dimensional plasma cavity that is defined by source, drain, and multiple gates of a GaAs/AlGaAs high electron mobility transistor. Both narrow-band terahertz detection and a rich harmonic spectrum are evident. With a bolometric sensor in the channel, we report responsivity, on resonance at 235–240 GHz and at 20 K, of up to 7 kV/W and a noise equivalent power of 5×10−10 W/Hz1/2.