Could we detect neutrinos from a supernova in Andromeda? Are our neutrino detectors sensitive enough to do so? They detected 13 neutrinos from SN1987A, which was 186,000 light years away, but our detectors are much more sensitive now.
The first supernova from which neutrinos have been detected was SN 1987A in the large magellanic cloud at roughly 51kpc distance - like you write. Current detectors are not sensitive enough to detect signals beyond this distance; however the next generation of detectors (when built) is expected to be sensitive to supernovas around the distance of Andromeda (e.g. see this paper by Wigmans (2018), §9.1).