The generator matrix

 1  0  0  1  1  1  0  1  1  1  0  1  X  0  1  1  1  0  1  0  X  0  1  1  1  1  1  1  0  1  0  1  1  1  X  X  1  1  1  1
 0  1  0  1  0  1  1  0  0  1  1 X+1  1  0  0  X  1  1 X+1  0  1  X  1  X  0  1  0  1  1  1  1  0  0  0  0  X  1  1  X  0
 0  0  1  1  1  0  1  0  1  1  X  0 X+1  1  0  1  1  0  0  1  1  1  X X+1  0  1  1  X  0  0 X+1  1 X+1 X+1  1  1  0  X  1  0
 0  0  0  X  0  0  0  0  0  0  X  X  X  0  0  0  0  X  0  X  X  X  0  X  0  X  X  0  X  X  X  0  X  0  X  X  X  0  0  0
 0  0  0  0  X  0  0  0  0  0  X  X  0  X  0  0  0  X  X  0  0  0  X  X  0  X  0  X  X  X  X  X  0  0  0  X  0  X  0  0
 0  0  0  0  0  X  0  0  0  0  0  X  0  0  0  0  X  X  X  X  X  0  X  0  X  0  X  0  0  X  0  X  X  X  0  X  0  X  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  X  X  0  X  X  0  X  X  X  X  X  X  X  X  X  0  X  0  0  0  X  0  0  X  0  0
 0  0  0  0  0  0  0  X  0  0  0  X  X  X  X  0  X  X  X  X  0  0  0  X  X  0  0  X  X  0  X  0  X  0  X  0  X  X  0  0
 0  0  0  0  0  0  0  0  X  0  X  X  0  X  X  X  X  X  0  X  X  X  X  X  0  0  0  X  0  X  X  0  0  X  0  X  0  0  0  0
 0  0  0  0  0  0  0  0  0  X  X  X  X  0  X  X  X  X  X  0  0  X  0  0  X  X  0  X  0  0  0  X  X  X  0  0  X  X  X  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+32x^28+24x^29+92x^30+102x^31+195x^32+228x^33+322x^34+364x^35+433x^36+570x^37+615x^38+740x^39+699x^40+736x^41+628x^42+624x^43+498x^44+404x^45+287x^46+198x^47+150x^48+76x^49+90x^50+20x^51+29x^52+10x^53+13x^54+11x^56+1x^62

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 4.35 seconds.