The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  X  0  1  1  1  0  1  X  0  0  1  0  1  0  1  1  1  1  0  X  0  1  0  0  X  1  1  1
 0  1  0  1  0  1  1  0  0  1  1  1  1  X  X  X  1  1 X+1  1  0  0  X  1 X+1  0  X X+1 X+1  0  1  1  0  X  1  1  0  0 X+1 X+1
 0  0  1  1  1  0  1  0  1  1  0  X  1  1  1  0  1  0  0 X+1  1  1  1  0  X  1  X  0  1 X+1 X+1 X+1  1  0  1  0  1  0  0  0
 0  0  0  X  0  0  0  0  0  0  0  X  0  X  0  X  0  X  0  0  0  0  0  X  X  X  X  0  0  0  0  X  X  0  X  X  X  0  X  X
 0  0  0  0  X  0  0  0  0  0  0  X  X  0  X  X  0  0  0  0  X  X  X  0  0  0  0  0  X  0  X  0  X  X  X  0  0  X  X  X
 0  0  0  0  0  X  0  0  0  0  0  0  X  X  0  X  0  0  X  0  X  0  X  0  0  X  0  0  X  X  X  X  0  0  X  0  X  0  X  X
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  0  0  0  0  X  X  0  X  0  X  X  X  0  X  X  0  X  0  0  0  0  0  X  0  X  X
 0  0  0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  X  0  X  0  0  X  X  0  0  X  X  X  0  X  X  X  X  X  0  X  X  0  0
 0  0  0  0  0  0  0  0  X  0  0  X  X  0  X  X  X  X  X  X  0  0  0  X  0  X  X  0  X  0  X  0  0  0  X  0  X  0  0  0
 0  0  0  0  0  0  0  0  0  X  0  X  0  X  0  X  X  0  X  X  X  X  0  0  X  X  X  X  0  X  X  0  X  0  X  X  X  X  0  0
 0  0  0  0  0  0  0  0  0  0  X  0  X  X  0  X  X  X  0  X  0  X  X  0  X  X  0  0  0  X  0  X  X  X  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+151x^28+218x^30+759x^32+1000x^34+2112x^36+2278x^38+3165x^40+2512x^42+2166x^44+982x^46+691x^48+168x^50+144x^52+10x^54+23x^56+3x^60+1x^64

The gray image is a linear code over GF(2) with n=80, k=14 and d=28.
This code was found by Heurico 1.16 in 17.3 seconds.