The realization space is
  [0   1   1   0   0   1   4*x1 + 4   4*x1 + 4   8*x1^2 + 16*x1 + 8        4*x1 + 4      x1 + 1]
  [1   1   0   1   0   0       8*x1      16*x1                32*x1            8*x1        4*x1]
  [1   1   0   0   1   1          0       8*x1      16*x1^2 + 16*x1   4*x1^2 + 4*x1   x1^2 + x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-512*x1^9 + 2048*x1^8 + 7680*x1^7 + 4096*x1^6 - 5632*x1^5 - 6144*x1^4 - 1536*x1^3)
avoiding the zero loci of the polynomials
RingElem[2, x1, x1 - 1, x1^2 - 4*x1 - 1, 3*x1 - 1, x1 + 1, x1 - 3, 3*x1 + 1, 2*x1 + 1, x1^2 - 2*x1 - 1]