Narrow linewidth and fast-chirped frequency are essential in frequency-modulated continuous-wave lasers. We introduce a laser that meets these requirements by coupling a distributed feedback laser with an external high-Q microring resonator, where a bulky stacked piezoelectric chip is attached to the resonator for fast tuning. The laser demonstrates an ultranarrow intrinsic linewidth of 22 Hz in the self-injection-locked state. Actuated by the bulky piezoelectric chip, the maximum triangular actuation bandwidth can reach 100 kHz. The driving voltage is filtered to avoid a resonant mechanical mode, obtaining the minimum residual linearity error at 10 kHz with a 4.2 GHz tuning range. A light detection and ranging system was set up for a proof-of-concept experiment, demonstrating a high detection precision with standard deviations of 2.7 and 4.0 cm for targets at 15 and 30 m, respectively.