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