A search for heavy neutral lepton (N) production in K+→e+Ndecays using the data sample collected by the NA62 experiment at CERN in 2017–2018 is reported. Upper limits of the extended neutrino mixing matrix element |Ue4|^2 are established at the level of 10^−9 over most of the accessible heavy neutral lepton mass range 144–462 MeV/c2, with the assumption that the lifetime exceeds 50 ns. These limits improve significantly upon those of previous production and decay searches. The |Ue4|^2 range favoured by Big Bang Nucleosynthesis is excluded up to a mass of about 340 MeV/c2.