3D asymmetries are major performance-degradation mechanisms in ICF implosions at the NIF. These asymmetries can be diagnosed with the three neutron imaging systems fielded with orthogonal views to the implosion. Conventional tomographic reconstructions are typically used to reconstruct the 3D morphology of the hot-spot and surrounding dense fuel in an implosion using neutron images, but the problem is ill-posed with only three imaging lines of sight. In this work, a 3D reconstruction technique has been developed and used to overcome these limitations by combining information from the neutron images, neutron activation data, and neutron spectra. Markov chain Monte Carlo is used to fit a physics model to the observed data to robustly reconstruct the 3D morphology of the hot-spot and dense fuel in a NIF implosion. This technique is used to infer that mode-3 was especially impactful on NIF shot N240628. This technique will be used to help minimize asymmetries in ICF implosions.