The realization space is
  [1   1   0     x3   0   1   1    0      x3    1    1]
  [1   0   1   x2^2   0   1   0    1    x2^2   x2   x2]
  [0   0   0      0   1   1   1   x1   x2*x3   x2   x3]
in the multivariate polynomial ring in 3 variables over ZZ
avoiding the zero loci of the polynomials
RingElem[x2 - 1, x2 - x3, x2, x1*x2 - x3, x1*x2 - x1 - x3, x1, x1*x2^2 - x1*x2*x3 + x3^2, x1*x2 - x1 - x3 + 1, x1*x2 - x3 + 1, x2 + x3 - 1, x3 - 1, x2*x3 - x2 + x3, x2^2*x3 - x2^2 + x2*x3 - x3^2, x2^2 - x3, x3, x1*x2 - x1 - x2, x1 - 1, x1*x2 - x1*x3 + x3, x1*x2 - x2 + 1, 2*x2 - 1, x2^2 - x2 + x3, x1*x2^2 - x1*x3 - x2*x3, x1*x2^2 - x1*x3 - x2*x3 + x3, x1*x2^2 - x2*x3 + x3, x2^2 + x2*x3 - x3, x1 + 1, x1*x2^2 + x3, x1*x2^2 - x1*x3 + x3]