  We measured the production of \nuc{57}{Co}, \nuc{54}{Mn}, \nuc{68}{Ge},
\nuc{65}{Zn}, and \nuc{60}{Co} in a sample of Ge enriched in isotope 76 due to
high-energy neutron interactions. These isotopes, especially \nuc{68}{Ge}, are
critical in understanding background in Ge detectors used for double-beta decay
experiments. They are produced by cosmogenic-neutron interactions in the
detectors while they reside on the Earth's surface. These production rates were
measured at neutron energies of a few hundred MeV. We compared the measured
production to that predicted by cross-section calculations based on CEM03.02.
The cross section calculations over-predict our measurements by approximately a
factor of three depending on isotope. We then use the measured cosmic-ray
neutron flux, our measurements, and the CEM03.02 cross sections to predict the
cosmogenic production rate of these isotopes. The uncertainty in extrapolating
the cross section model to higher energies dominates the total uncertainty in
the cosmogenic production rate.
