The Monte Carlo theory provides a powerful tool for solving three-dimensional neutron shielding problems. Special variance reducing methods must be applied if the detector regions are very remote from the source region. Recently, an idea for a new scoring method was proposed to reduce an estimator for large distances between flux point and collision point to the standard flux point estimator. A Monte Carlo code based on this method was developed. This code was applied to the calculation of neutron doses, neutron spectra, and neutron fluxes produced by the detonation of an enhanced radiation weapon. The results may be considered as a test of the efficiency and as a first application of a new Monte Carlo method. The radiation doses reported in this Note only refer to neutrons. The gamma-ray radiation doses due to neutron capture reactions are not considered.