Full configuration interaction quantum Monte Carlo seems like it is poised to overtake DFT in some applications pretty soon. I am curious if there is any freely available implementation of the method, as I cannot seem to find one.
I don't know any production implementation that is released in a free and open-source package. However, a few codes appear to be developing this capability. You might try to write your own or modify an existing robust code that supports CI already to do this. I'd recommend PSI4 if you decide to go that route.
There are, to my knowledge, two codes available:
Both are developed by the authors involved in the design of FCIQMC. The second one has a better documentation and also includes other recent methods like i-FCIQMC, CCMC, DMMC or semi-stochastic MC.
These methods are intended to compete with wavefunction methods on accuracy but with a lower computational complexity. For example, i-FCIQMC has been reported for ethene and butadiene molecules (http://doi:10.1021/ct300486d), that otherwise are impossible to treat with Full Configuration Interaction. In fact the later cannot go beyond dinitrogen ($N_2$) with a decent basis set. On the other hand this is not always possible. For strongly correlated systems you will have to explore almost all the Hilbert space, then you gain only a slight or no benefit from using them. Improvements are part of current research.
Since the authors claim that their calculations were done with these codes I would expect the results reported in the literature to be reproducible.