A search for heavy neutral lepton production in K + decays using a data sample collected with a minimum bias trigger by the NA62 experiment at CERN in 2015 is reported. Upper limits at the 10 − 7 to 10 − 6 level are established on the elements of the extended neutrino mixing matrix | U e 4 | 2 and | U μ 4 | 2 for heavy neutral lepton mass in the ranges 170–448 MeV/ c 2 and 250–373 MeV/ c 2 , respectively. This improves on the previous limits from HNL production searches over the whole mass range considered for | U e 4 | 2 , and above 300 MeV/ c 2 for | U μ 4 | 2 .