The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X X 1 1 X X 1 1 X 1 X
0 X 0 0 0 0 0 0 0 0 0 X 0 0 X X 0 0 0 0 X X X X X X 0 0 X X X X 0 X X 0
0 0 X 0 0 0 0 0 0 0 0 X X X X X 0 0 0 X X 0 0 X 0 0 X X 0 0 X 0 X 0 0 X
0 0 0 X 0 0 0 0 0 0 X 0 X X 0 X X 0 X 0 X X X 0 X X X 0 0 X X 0 0 0 0 X
0 0 0 0 X 0 0 0 0 0 X 0 0 X X X X X 0 X 0 0 0 0 0 X 0 0 X X X X X X 0 X
0 0 0 0 0 X 0 0 0 X 0 0 0 X X 0 X 0 X X X 0 0 X X X X 0 0 0 0 0 0 X 0 X
0 0 0 0 0 0 X 0 0 X 0 0 X 0 0 X X X 0 X X 0 X X X 0 0 X 0 X 0 X X X 0 0
0 0 0 0 0 0 0 X 0 X X X X 0 0 0 0 0 X X X X X X 0 X X X X X X 0 X 0 X X
0 0 0 0 0 0 0 0 X X X X 0 0 X X X 0 0 0 X 0 0 0 0 0 X 0 0 X 0 X X 0 X X
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+87x^28+16x^30+183x^32+112x^34+250x^36+112x^38+153x^40+16x^42+75x^44+14x^48+4x^52+1x^56
The gray image is a linear code over GF(2) with n=72, k=10 and d=28.
This code was found by Heurico 1.16 in 0.131 seconds.