Neutrino communications could travel into every nook and cranny, very fast and far indeed.
If you can easily modulate the source of your signal as is the case with the neutron source, it becomes as uninteresting as morse code.
The real issue is the detection end. Because of how little neutrinos interact with matter, you need a lot of neutrinos to pass through a detector before you can expect to see a signal, and then you need to distinguish that signal from noise.
Neutrino detectors work because there is an astronomically small but non-zero chance that a neutrino emit either a Z or W boson. A Z boson can hit a nearby electron, accelerating it, or a W boson can decay into a fast moving electron, either of which can be observed in various ways. There's no way to prompt this behavior, but if you're watching enough matter while enough neutrinos are passing through, eventually you'll see some events. The number of events are proportional to how many neutrinos are passing through, so if you see a large number of events in a short period of time, you know something has sent a pulse of neutrinos.
That said, you could most certainly have a muon beam neutrino detector located at the same site as a neutrino detector, allowing you to both send and receive messages. Because the neutrino beam is highly directional, it won't interfere with the detector.
Needless to say this is woefully impractical, would require an extremely large neutrino flux and detector, and would have an absolutely abysmal bit-rate. Not to mention you'd likely only be able to send messages in one direction. But it could be done.
see: https://www.fnal.gov/pub/today/archive/archive_2014/today14-...