The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  1  0  1  1  X  0  1  1  0  X  1  1  1  1  1  0  0  1  0  1  0  1  X  0  1  1  1
 0  1  1  0  1  1  0  1  1  0 X+1  1  0 X+1  1  0 X+1  1  1 X+1 X+1  1  1  X  0  1  1  0  1  1  0  1 X+1  1 X+1  X  1  0  0  0
 0  0  X  0  0  0  0  0  0  0  0  0  X  0  0  X  X  0  0  0  0  X  0  0  X  X  X  X  0  X  X  X  X  0  X  X  X  0  0  0
 0  0  0  X  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  0  0  X  X  0  0  0  0  0
 0  0  0  0  X  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  X  0  0  X  X  0  X  0  0  0  0  0  0  X  0  0  0  0
 0  0  0  0  0  X  0  0  0  0  0  X  0  X  X  0  X  0  X  0  X  X  0  0  X  X  0  0  0  X  X  X  X  X  0  X  0  0  0  0
 0  0  0  0  0  0  X  0  0  0  0  X  0  0  X  X  X  X  0  0  X  0  X  X  X  0  0  0  X  0  X  0  X  0  0  0  X  0  0  0
 0  0  0  0  0  0  0  X  0  0  X  0  0  0  X  0  X  X  X  0  0  X  X  0  X  X  X  0  0  0  0  X  X  0  X  0  0  0  0  0
 0  0  0  0  0  0  0  0  X  0  X  X  X  0  0  0  X  X  X  X  X  X  0  0  X  0  X  0  X  X  X  X  0  0  X  X  0  X  X  0
 0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  0  X  X  0  0  X  0  0  X  0  X  X  X  X  0  X  X  0  0  0  X  0  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+46x^28+37x^30+28x^31+142x^32+94x^33+154x^34+174x^35+237x^36+304x^37+255x^38+424x^39+298x^40+412x^41+297x^42+316x^43+200x^44+192x^45+178x^46+76x^47+87x^48+22x^49+76x^50+6x^51+13x^52+23x^54+1x^58+3x^62

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 1.34 seconds.