The realization space is
  [1   1   0   0   1                x3*x4    0      x2    1    1]
  [0   1   1   0   0                x3*x4    1   x3*x4   x3   x3]
  [0   0   0   1   1   x2*x4 - x2 + x3*x4   x1   x2*x4   x2   x4]
in the multivariate polynomial ring in 4 variables over ZZ
avoiding the zero loci of the polynomials
RingElem[x3, x2 - x4, x3 - 1, x4, x4 - 1, x2 - x3*x4, x1, x1*x3 - x4, x1*x3 - x1 - x4, x1*x3 - x4 + 1, x1*x3^2*x4 - x1*x3*x4 + x2*x4 - x2 - x3*x4^2 + x3*x4, x2*x4 - x2 + x3*x4 - x4^2, x2*x4 - x2 + x3*x4, x3 + x4 - 1, x1*x3 - x2, x1*x3 - x1 - x2, x1*x3 - x2 + 1, x1*x3^2*x4 - x1*x3*x4 - x2*x3*x4 + x2*x4 - x2 + x3*x4, x2*x3*x4 - x2*x4 + x2 - x3*x4, x2 + x3 - 1, x2 - 1, x2, x1*x2 - x1*x3*x4 + x2*x4, x1*x3*x4 - x2*x4 + x2, x1*x3*x4 - x2*x4 + x2 - x3*x4, x1 + 1]