The realization space is
  [1   0   1   0   1    0   1     1     1       1]
  [0   1   1   0   0    1   1    x1   -x1      x1]
  [0   0   0   1   1   -1   1   -x1   -x1   -3*x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (8*x1^4 - 6*x1^3 - 2*x1^2)
avoiding the zero loci of the polynomials
RingElem[2, x1, 2*x1 + 1, x1 + 1, x1 - 1, 3*x1 + 1, 3]