In DigitalOcean's Engineering team, they implemented a solution to manage package versions and dependencies in their Go code bases by creating a single Git repository, called a mono repo. This approach eliminates the need for an external management tool and allows all projects to share the same version of packages. The mono repo is structured with two main directories: `docode` for the team's own code and `third_party` for third-party code. By setting the `GOPATH` environment variable to point to these directories, developers can access their dependencies without having to manage versions explicitly. While there are some caveats, such as dealing with Git sub-modules issues, the mono repo has proven to be a simple and effective solution for managing package versions and dependencies in their Go code bases.