Summary, as I understand it: The connectome for C. elegans's 302-neuron brain has been known for some time, but actually doing anything with it (especially actually understanding it) has proved troublesome, especially because there could easily be relevant information about its brain function not stored in just the connections of the neurons.
However, the OpenWorm project -- which is trying to eventually make much more detailed C. elegans simulations, including an appropriate body -- recently tried just fudging it and making a simulation based on the connectome anyway, though in a wheeled body rather than a wormlike one. And the result does seem to act at least somewhat like a C. elegans worm, though I am not really one to judge that. (Video is here.)
I'm having trouble finding much more information about this at the moment. I don't know if they've actually yet released detailed technical information.