The realization space is
  [1   1   0   6   0   1   1   0   6   3   3]
  [0   1   1   1   0   0   1   1   1   1   1]
  [0   0   0   0   1   1   1   2   4   2   1]
in the integer ring
within the vanishing set of the ideal
264ZZ
avoiding the zero loci of the polynomials
RingElem[2, 5, 3, 7]