The realization space is
  [1   1   0   2   1   0   5    0    1    2    2]
  [0   1   1   1   0   0   0    1   -2    2    1]
  [0   0   0   0   1   1   1   -1    1   -1   -1]
in the integer ring
within the vanishing set of the ideal
220ZZ
avoiding the zero loci of the polynomials
RingElem[3, 7, 2, 5]