As Artificial Intelligence (AI) has flourished in various industries in recent years, the evolutionary trend of endogenous network intelligence continues to accelerate. Connected intelligence, which aims to achieve a widely distributed and collaborative evolution of intelligence, has received much attention. Meanwhile, the emerging Computing Power Network (CPN) provides more robust computation and communication capabilities for intelligence training and intelligent application processing. In this context, the integration of CPN and connected intelligence becomes a potential solution to drive the digital and intelligent transformation of networks. In this paper, we propose a scheme to jointly consider task scheduling, routing, and intelligence capability improvement during the processing of smart applications represented by Digital Twin (DT) in the CPN-enabled connected intelligence systems. We formulate the problem of jointly optimizing the processing time consumption and training accuracy improvement. We solve the problem using a modified NSGA-II algorithm and numerical results show that our approach is effective in optimizing the overall average time consumption and improving the accuracy of the intelligence models distributed in the system during task processing.