The emergence of parallel convolution-operation technology has substantially powered the complexity and functionality of optical neural networks (ONN) by harnessing the dimension of optical wavelength. However, this advanced architecture faces remarkable challenges in high-level integration and on-chip operation. In this work, convolution based on time-wavelength plane stretching approach is implemented on a microcomb-driven chip-based photonic processing unit (PPU). To support the operation of this processing unit, we develop a dedicated control and operation protocol, leading to a record high weight precision of 9 bits. Moreover, the compact architecture and high data loading speed enable a preeminent photonic-core compute density of over 1 trillion of operations per second per square millimeter (TOPS mm^-2). Two proof-of-concept experiments are demonstrated, including image edge detection and handwritten digit recognition, showing comparable processing capability compared to that of a digital computer. Due to the advanced performance and the great scalability, this parallel photonic processing unit can potentially revolutionize sophisticated artificial intelligence tasks including autonomous driving, video action recognition and image reconstruction.