Right solver for JuMP to find every solution of a linear system of equations with integer solutions

Specific Domains Optimization (Mathematical)
,
14

There are the 24 solutions (returned by Mathematica):

0,0,0,0,0,0,1,1,1,2,0,0,1,0,0,0
0,0,0,0,0,0,1,1,2,1,0,0,0,1,0,0
0,0,0,0,0,1,0,1,1,1,1,0,1,0,0,0
0,0,0,0,0,1,0,1,2,0,1,0,0,1,0,0
0,0,0,0,0,1,0,1,2,1,0,0,0,0,1,0
0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,0
0,0,0,0,0,1,1,0,2,0,0,1,0,1,0,0
0,0,0,0,0,1,1,0,2,1,0,0,0,0,0,1
0,0,0,0,0,2,0,0,1,0,1,1,1,0,0,0
0,0,0,0,0,2,0,0,2,0,0,1,0,0,1,0
0,0,0,0,0,2,0,0,2,0,1,0,0,0,0,1
0,0,0,0,1,0,0,1,0,2,1,0,1,0,0,0
0,0,0,0,1,0,0,1,1,1,1,0,0,1,0,0
0,0,0,0,1,0,0,1,1,2,0,0,0,0,1,0
0,0,0,0,1,0,1,0,0,2,0,1,1,0,0,0
0,0,0,0,1,0,1,0,1,1,0,1,0,1,0,0
0,0,0,0,1,0,1,0,1,2,0,0,0,0,0,1
0,0,0,0,1,1,0,0,0,1,1,1,1,0,0,0
0,0,0,0,1,1,0,0,1,0,1,1,0,1,0,0
0,0,0,0,1,1,0,0,1,1,0,1,0,0,1,0
0,0,0,0,1,1,0,0,1,1,1,0,0,0,0,1
0,0,0,0,2,0,0,0,0,1,1,1,0,1,0,0
0,0,0,0,2,0,0,0,0,2,0,1,0,0,1,0
0,0,0,0,2,0,0,0,0,2,1,0,0,0,0,1

I tried checking both solutions (yours and Mathematica) using sort with no avail. I’ll send the results soon, but I’m confident both are equal.