We introduce the moving mesh code Shadowfax, which can be used to evolve a mixture of gas, subject to the laws of hydrodynamics and gravity, and any collisionless fluid only subject to gravity, such as cold dark matter or stars. The code is written in C++ and its source code is made available to the scientific community under the GNU Affero General Public License. We outline the algorithm and the design of our implementation, and demonstrate its validity through the results of a set of basic test problems, which are also part of the public version. We also compare Shadowfax with a number of other publicly available codes using different hydrodynamical integration schemes, illustrating the advantages and disadvantages of the moving mesh technique.