The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  1  0  1  1  0  1  1  0  0  1  1  1  0  1  0  1  1  0  1  1  X  1  1  1  1  1  1
 0  1  1  0  1  1  0  1  1  0  1  1  0 X+1  1  0 X+1  1 X+1  0  1  1  X X+1 X+1  1 X+1  1 X+1  0  1  0  0  1  0  0  X X+1  0  0
 0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  X  0  0  X  X
 0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  0  0  X  0  0  X  X  X  0  0  0  0
 0  0  0  0  X  0  0  0  0  0  0  0  0  X  0  X  0  X  X  0  X  0  X  X  0  0  X  X  X  0  X  0  X  X  X  0  0  X  X  X
 0  0  0  0  0  X  0  0  0  0  0  0  0  X  X  X  X  X  0  X  0  X  X  0  0  X  X  X  0  0  X  X  0  0  0  X  0  X  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  X  0  X  X  X  X  X  X  0  0  X  0  0  X  0  0  0  X  0  0  X  X  X  X  X  X
 0  0  0  0  0  0  0  X  0  0  0  X  X  X  0  0  X  0  X  0  0  X  X  X  0  0  0  0  X  0  0  X  X  0  X  X  X  X  X  X
 0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  0  X  X  0  0  0  0  X  0  X  0  X  0  0  X  X  0  X  X  0  X  0  X  0  0
 0  0  0  0  0  0  0  0  0  X  0  X  0  0  X  X  0  0  0  0  0  0  X  X  X  X  0  0  X  X  0  0  X  X  X  0  X  0  0  0
 0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  X  0  X  X  0  X  X  0  X  X  0  X  0  0  X  0  0  X  0  0  0  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+117x^28+36x^30+443x^32+372x^34+1102x^36+1128x^38+1777x^40+1128x^42+1150x^44+372x^46+416x^48+36x^50+94x^52+18x^56+1x^60+1x^72

The gray image is a linear code over GF(2) with n=80, k=13 and d=28.
This code was found by Heurico 1.16 in 5.28 seconds.