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 $^{14}$Be into $^{10}$Be 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 $^{12, 14}$Be and $^{8}$He 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.