The realization space is
  [1   1   0    1   0   1   1   0    2    1    1]
  [1   0   1   -1   0   1   0   3   -2   -2   -3]
  [0   0   0    0   1   1   1   2   -1   -2   -2]
in the integer ring
within the vanishing set of the ideal
60ZZ
avoiding the zero loci of the polynomials
RingElem[2, 3, 5]