6G will revolutionize the software world allowing faster cellular communications and a massive number of connected devices. 6G will enable a shift towards a continuous edge-to-cloud architecture. Current cloud solutions, where all the data is transferred and computed in the cloud, are not sustainable in such a large network of devices. Current technologies, including development methods, software architectures, and orchestration and offloading systems, still need to be prepared to cope with such requirements. In this paper, we conduct a Systematic Mapping Study to investigate the current research status of 6G Software Engineering. Results show that 18 research papers have been proposed in software process, software architecture, orchestration and offloading methods. Of these, software architecture and software-defined networks are respectively areas and topics that have received the most attention in 6G Software Engineering. In addition, the main types of results of these papers are methods, architectures, platforms, frameworks and algorithms. For the five tools/frameworks proposed, they are new and not currently studied by other researchers. The authors of these findings are mainly from China, India and Saudi Arabia. The results will enable researchers and practitioners to further research and extend for 6G Software Engineering.