Next generation low-background experiments require a detailed understanding of all possible radiation backgrounds. One important radiation source are muon-induced neutrons. Their production processes are up to now not fully understood. New measurements with MINIDEX (Muon-Induced Neutron Indirect Detection EXperiment) of the production of neutrons by cosmogenic muons in high-Z materials are reported. The setup is located at the T{u}bingen Shallow Underground Laboratory, which provides a vertical shielding depth of (13.2,$pm$,0.8) meter water equivalent at the setup location. Muon-induced neutrons are identified by the detection of 2.2,MeV gammas from their capture on hydrogen with high-purity germanium detectors. The experimental results were compared to Geant4 Monte Carlo predictions. The measured rate of 2.2,MeV neutron capture gammas for lead was found to be in good agreement with the Geant4 predicted rate. For copper the measured rate was found to be a factor of 0.72,$pm$,0.14 lower than the Geant4 predicted rate. An additional simulation was performed using the FLUKA Monte Carlo code. The FLUKA predicted rate of detected 2.2,MeV neutron capture gammas for lead was also found to be in good agreement with the experimental value. A detailed comparison of muon interactions and neutron production in lead for Geant4 and FLUKA revealed large discrepancies in the description of photo-nuclear and muon-nuclear inelastic scattering reactions for muon energies at shallow underground sites. These results suggest that Geant4, when used with Geant4 recommended or standard physics lists, underpredicts the neutron production in photo-nuclear inelastic scattering reactions while at the same time it overpredicts the neutron production in muon-nuclear inelastic scattering reactions.
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