The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  X  1  0  1  1  0  0  X  1  0  0  X  1  1  1  0  X  0  1  1  0  X  0  X  0  1  1  0  1
 0  1  0  0  0  0  0  0  0 X+1  1  1  0  1  1 X+1  1  1  1  X  0  X  1  X  1  1  X  1  1 X+1 X+1  1  0  X  1  0  0 X+1  1  X
 0  0  1  0  0  0  1  1  1  1  1  0  X  1  X  X  1  1  1 X+1  X  1  X  1 X+1  1  1  1  X  X  X  0  X  1  0  1  0  X  1  0
 0  0  0  1  0  1  1  0  1  0  0  0  1  X  1  0  1 X+1  X  X  1  0  1 X+1  1 X+1  1  X  1  1  1  0  0  0  1  X  X  0  0 X+1
 0  0  0  0  1  1  0  1  1 X+1  X X+1  0 X+1  0  0  1  X  X  0 X+1  1  1 X+1  X X+1  0  X  0 X+1  1  0  1 X+1  X  X  1  1  X  X
 0  0  0  0  0  X  0  0  0  X  X  0  X  0  X  0  X  X  0  X  X  X  0  X  0  X  0  X  0  0  0  0  0  0  X  X  X  0  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  X  0  0  X  X  X  0  0  0  0  0  X  X  0  X  X  0  X  X  0  0
 0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  X  X  X  0  X  0  X  0  X  0  X  X  0  X  X  X
 0  0  0  0  0  0  0  0  X  0  X  X  X  0  0  X  0  X  0  0  X  0  0  X  X  0  X  0  X  0  X  0  X  X  X  X  X  0  0  0

generates a code of length 40 over Z2[X]/(X^2) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+46x^29+132x^30+256x^31+414x^32+478x^33+623x^34+782x^35+953x^36+1090x^37+1222x^38+1380x^39+1391x^40+1468x^41+1391x^42+1164x^43+1003x^44+818x^45+588x^46+456x^47+285x^48+182x^49+129x^50+54x^51+43x^52+14x^53+10x^54+4x^55+5x^56+1x^58+1x^60

The gray image is a linear code over GF(2) with n=80, k=14 and d=29.
This code was found by Heurico 1.16 in 32.9 seconds.