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.