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