The realization space is
  [1   1   0   3   0   1   1    0   3   3   3]
  [0   1   1   4   0   0   1    2   4   2   2]
  [0   0   0   0   1   1   1   -1   2   1   2]
in the integer ring
within the vanishing set of the ideal
20ZZ
avoiding the zero loci of the polynomials
RingElem[2, 3, 5]