The generator matrix
1 0 0 1 1 1 0 1 1 1 1 1 0 X 0 1 0 1 1 0 1 1 0 X X X 1 1 X 1 X 1 X 0 1 1
0 1 0 1 0 1 1 0 0 1 X+1 X 1 1 0 X 0 X+1 X 1 X+1 X+1 1 X 1 0 X 1 1 X+1 0 0 1 1 X+1 X
0 0 1 1 1 0 1 0 1 X+1 X 1 X 1 1 0 1 X+1 X X 0 0 0 1 1 1 X+1 X X+1 X 1 0 X+1 X X+1 X+1
0 0 0 X 0 0 0 0 0 X 0 0 0 0 0 0 0 X 0 X X X X X 0 0 X X 0 X 0 X 0 X 0 X
0 0 0 0 X 0 0 0 0 0 0 0 X X X X 0 X 0 0 X 0 X X X 0 0 X X 0 0 X 0 0 0 X
0 0 0 0 0 X 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X X X X X X 0 X 0 0 X X X X X 0
0 0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 X X X X X 0 0 0 X 0 X X X 0 X X X 0 0 0
0 0 0 0 0 0 0 X 0 X X X 0 0 X 0 X X X 0 X 0 X 0 0 0 0 0 X 0 X X X X 0 X
0 0 0 0 0 0 0 0 X 0 0 X X X X X 0 X 0 X 0 X 0 0 0 0 X X 0 0 X X 0 0 X 0
generates a code of length 36 over Z2[X]/(X^2) who´s minimum homogenous weight is 28.
Homogenous weight enumerator: w(x)=1x^0+204x^28+298x^30+567x^32+576x^34+772x^36+660x^38+572x^40+240x^42+156x^44+18x^46+28x^48+4x^52
The gray image is a linear code over GF(2) with n=72, k=12 and d=28.
This code was found by Heurico 1.16 in 15.3 seconds.