The generator matrix

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

generates a code of length 40 over Z2[X]/(X^2) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+66x^30+92x^31+221x^32+290x^33+315x^34+454x^35+470x^36+554x^37+594x^38+670x^39+685x^40+600x^41+697x^42+654x^43+489x^44+428x^45+313x^46+230x^47+166x^48+110x^49+56x^50+12x^51+13x^52+2x^53+7x^54+2x^56+1x^64

The gray image is a linear code over GF(2) with n=80, k=13 and d=30.
This code was found by Heurico 1.10 in 1.56 seconds.