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 1 1 1 1 X 1 X 1 1 1 1 X X 1 1
0 X 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X X X X X X 0 0 X X X X 0 0 X X
0 0 X 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 X X X X X X 0 0 X X 0 X 0 X X 0 X X X X X
0 0 0 X 0 0 0 0 0 0 0 0 0 X 0 0 0 X X X X X X X 0 X 0 X X X 0 X X 0 X 0 0 0 0 0
0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 X X X X X X 0 X X X 0 0 X 0 0 X 0 0 0 0 0 X 0 0 0
0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 X X 0 X X 0 X 0 X X X X 0 0 0 X 0 X X 0 X 0 X X X
0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 X X X X 0 X X 0 0 0 X X X 0 0 X 0 X 0 0 X 0 X X
0 0 0 0 0 0 0 X 0 0 0 X 0 0 0 0 X X 0 X 0 0 0 X X 0 X X 0 X X X 0 X 0 X 0 0 0 0
0 0 0 0 0 0 0 0 X 0 0 X 0 0 0 X 0 0 X 0 X 0 0 X X 0 0 X X X 0 0 0 X X 0 X X X X
0 0 0 0 0 0 0 0 0 X 0 X X X X X 0 0 0 X 0 0 X X 0 X 0 X X X X 0 X 0 0 0 X 0 0 0
0 0 0 0 0 0 0 0 0 0 X X X X X 0 0 X X X X X 0 X X X X X 0 X X 0 0 0 0 X X X 0 0
generates a code of length 40 over Z2[X]/(X^2) who´s minimum homogenous weight is 28.
Homogenous weight enumerator: w(x)=1x^0+118x^28+275x^32+32x^34+597x^36+480x^38+1094x^40+480x^42+600x^44+32x^46+276x^48+90x^52+18x^56+2x^60+1x^68
The gray image is a linear code over GF(2) with n=80, k=12 and d=28.
This code was found by Heurico 1.16 in 1.8 seconds.