The realization space is
  [1   0   1   2   0   1   1    0    1    2    1]
  [0   1   1   1   0   0   0    1    1   -1   -2]
  [0   0   0   0   1   1   2   -1   -2    2    2]
in the integer ring
within the vanishing set of the ideal
48ZZ
avoiding the zero loci of the polynomials
RingElem[2, 3, 5]