The realization space is
  [1   0   1   1   0   1   0   1   1   1]
  [0   1   1   4   1   1   0   2   0   4]
  [0   0   0   0   1   1   1   1   2   2]
in the multivariate polynomial ring in 0 variables over ZZ
avoiding the zero loci of the polynomials
RingElem[2, 3]