During my thesis and postdoc years I have produced several implementations of cosmological models in different codes:

- Hi_CLASS: Horndeski in the Cosmic Linear Anisotropy Solving System (with E. Bellini, P. Ferreira, J. Lesgourgues and I. Sawicki)
- Voids Over the Sky (VOS) a C++ code to compute the (non-linear) effects of cosmic voids on gravitational lensing, the ISW effect and other observables (used in 1201.2790)
- A modified version of Latticeeasy to solve the non-linear equations describing disformally coupled theories (with Y. Murakami, D. Bettoni)
- Quintessence in CLASS, already integrated in the public version
- Other codes for LTB models, disformally coupled DE, disformal quintessence and entropic gravity in CMBEasy

You can also visit my Github page to see what I have made public or email me if you are interested in codes not released yet.

Some codes that I like:

My codes of choice to obtain predictions for models representing fundamental physics are CLASS and CMBEasy (the latter one becoming less useful, as it is not maintained). Although I use it less, I find the CAMB online tool very useful.

There are two excelent packages for Mathematica that I strongly recommend:
xAct is able to handle symbolic computations within differential geometry in a very general way, but it is difficult to learn. RGTC is very easy to learn, but limited to tensor computations in a given set of coordinates.