Stochastic weather generators (SWGs) are digital twins of complex weather processes and widely used in agriculture and urban design. Due to improved measuring instruments, an accurate SWG for high-frequency precipitation is now possible. However, high-frequency precipitation data are more zero-inflated, skewed, and heavy-tailed than common (hourly or daily) precipitation data. Therefore, classical methods that either model precipitation occurrence independently of their intensity or assume that the precipitation follows a censored meta-Gaussian process may not be appropriate. In this work, we propose a novel multi-site precipitation generator that drives both occurrence and intensity by a censored non-Gaussian vector autoregression model with skew-symmetric dynamics. The proposed SWG is advantageous in modeling skewed and heavy-tailed data with direct physical and statistical interpretations. We apply the proposed model to 30-second precipitation based on the data obtained from a dense gauge network in Lausanne, Switzerland. In addition to reproducing the high-frequency precipitation, the model can provide accurate predictions as the long short-term memory (LSTM) network but with uncertainties and more interpretable results.