The generator matrix

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

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+48x^29+143x^30+250x^31+373x^32+498x^33+632x^34+826x^35+921x^36+1064x^37+1286x^38+1314x^39+1404x^40+1480x^41+1345x^42+1208x^43+1036x^44+788x^45+583x^46+418x^47+318x^48+198x^49+102x^50+78x^51+42x^52+20x^53+4x^54+2x^55+1x^58+1x^68

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 32.7 seconds.