The realization space is
  [1   1   0   2   0   1   1          0   4*x1 - 2   4*x1 - 4          2]
  [1   0   1   1   0   1   0   2*x1 - 1   2*x1 - 1   2*x1 - 1   2*x1 - 1]
  [0   0   0   0   1   1   1   2*x1 - 2       2*x1   2*x1 - 2       2*x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-4096*x1^6 + 16384*x1^5 - 25600*x1^4 + 19456*x1^3 - 7168*x1^2 + 1024*x1)
avoiding the zero loci of the polynomials
RingElem[2*x1 - 1, 2*x1 - 3, x1 - 2, 2, x1 - 1, x1, 4*x1 - 3, 3*x1 - 2]