We present a telecommunication-compatible photoconductive terahertz detector realized without using any short-carrier-lifetime photoconductor. By utilizing plasmonic contact electrodes on a thin layer of high-mobility photoconductor, the presented detector offers a short transit time for the majority of the photocarriers in the absence of a short-carrier-lifetime photoconductor. Consequently, high-sensitivity terahertz detection is achieved with a record-high signal-to-noise ratio of 122 dB over a 3.6 THz bandwidth under an optical probe power of 10 mW. To achieve such a high sensitivity, the device geometry is chosen to maintain a high resistance and low Johnson Nyquist noise. This design approach can be widely applied for terahertz detection using various semiconductors and optical wavelengths, without being limited by the availability of short-carrier-lifetime photoconductors.