The realization space is
  [1   1   0   2   1   0   2    0    2    1    2]
  [0   1   1   3   0   0   0    1   -3    1    3]
  [0   0   0   0   1   1   1   -1    2   -1   -2]
in the integer ring
within the vanishing set of the ideal
18ZZ
avoiding the zero loci of the polynomials
RingElem[2, 3, 5, 7]