A new approach to the production and detection of multineutrons, based on breakup reactions of beams of very neutron-rich nuclei, is presented. The first application of this technique to the breakup of 14Be into 10Be and 4n revealed 6 events consistent with the formation of a bound tetraneutron. The description of these data by means of an unbound-tetraneutron resonance is also discussed. The experiments that have been undertaken at GANIL in order to confirm this observation with 12, 14Be and 8He beams are presented. Details and illustrations related to this contribution can be found in the conference page at https://www.phy.ornl.gov/enam04/WebTalks/Mo-1.html.