The realization space is
  [1   1   1   0   0   1   2   2   1   0]
  [0   1   2   1   0   0   0   2   2   2]
  [0   0   0   0   1   1   1   1   1   1]
in the multivariate polynomial ring in 0 variables over ZZ
within the vanishing set of the ideal
Ideal (-20)
avoiding the zero loci of the polynomials
RingElem[2, 3]