For my simulations I use the free, open-source Einstein Toolkit code, which is based on the Cactus infrastructure. During my PhD, I built a module called FLRWSolver to feed cosmological initial data into the Einstein Toolkit. FLRWSolver is publicly available at this repository. Instructions to download and compile the Einstein Toolkit and incorporate FLRWSolver can be found here, and a brief tutorial on running a simple simulation can be found here. Feel free to contact me with any issues getting started with the code. To extract interesting things from Cactus in post-processing we use the analysis code mescaline (which will be made public in the future).
A set of simulation data from my PhD is freely available for download here. I am happy to share more current simulation data (which is honestly more easy to use) on reasonable request. Please don't hesitate to contact me about getting access to this.