The realization space is
  [1         x1   1   0   0   1         x1       2*x1    0        2*x1^2          2*x1^2]
  [1   3*x1 - 1   0   1   0   1   3*x1 - 1          0    1      3*x1 - 1        3*x1 - 1]
  [0          0   0   0   1   1   3*x1 - 1   3*x1 - 1   x1   3*x1^2 - x1   6*x1^2 - 2*x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (144*x1^8 - 384*x1^7 + 388*x1^6 - 188*x1^5 + 44*x1^4 - 4*x1^3)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, 2*x1 - 1, 3*x1 - 1, x1, 2*x1^2 + 3*x1 - 1, 2*x1 + 1, x1 + 1, 2, 2*x1^2 - 4*x1 + 1, 4*x1 - 1]