The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  0  1  X  1  1  0  X  1  X  0  1  1  1  1  1  0  0  X  1  X  1  1  1  X  0  1  1
 0  1  0  0  0  1  1  1  0  X X+1 X+1  1  1 X+1  X  X  1  X  1 X+1  1  1  X X+1  0  1  0  1  0  1  0  1  X  0  1  1  0 X+1  0
 0  0  1  0  1  1  0  1  0  1  1  X  0 X+1  X  1 X+1  0  0  0  X  1  X  1  1  X X+1  0  1  1  0  0  0 X+1  0  0 X+1  1  X  0
 0  0  0  1  1  0  1  1  1  0 X+1  X  1  0  1  1  0  1  1  X  0  X  X  1 X+1 X+1 X+1  0  0  1  1  1  X  0  0  X  X  X  X  0
 0  0  0  0  X  0  0  0  0  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  X  X  0  0  X
 0  0  0  0  0  X  0  0  0  0  0  0  X  X  X  0  X  0  X  X  0  X  0  0  X  0  X  X  X  0  X  X  X  X  X  X  0  X  X  X
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  X  X  X  0  0  X  X  X  0  X  0  X  X  0  X  0  0  X  0  0  X  0  X  X  0
 0  0  0  0  0  0  0  X  0  0  X  0  X  X  0  0  0  X  0  0  X  X  0  X  0  0  X  0  0  X  X  0  0  X  X  X  0  0  0  X
 0  0  0  0  0  0  0  0  X  X  X  X  X  X  0  X  X  0  0  0  X  X  0  0  X  X  X  0  X  0  X  X  0  X  X  0  0  X  0  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+72x^30+96x^31+184x^32+256x^33+372x^34+428x^35+520x^36+550x^37+574x^38+732x^39+650x^40+684x^41+606x^42+580x^43+512x^44+440x^45+348x^46+212x^47+161x^48+116x^49+69x^50+16x^52+2x^53+6x^54+4x^56+1x^66

The gray image is a linear code over GF(2) with n=80, k=13 and d=30.
This code was found by Heurico 1.16 in 4.82 seconds.