If this is, for example, a 17x17 lattice then we can model this. The spheres are tiny though, under 1mm and I can't imagine this amount and geometry reaching criticality. If this is a set problem and you have to solve it this way we can do it. If what you want is the answer from MCNP on a running reactor with this material as fuel I would suggest you homogenise. If you have a structure that is 10cm across, neutrons will not care much about the fine structure, only the quantities. Working out quantities of elements in bigger units and building the reactor from the big units is easier to model and needs less computer time.
So what are all the relevant parameters of the problem, what answers do you need and how do you want to solve it?