The generator matrix

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

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+80x^30+106x^31+238x^32+246x^33+365x^34+450x^35+485x^36+560x^37+568x^38+714x^39+574x^40+598x^41+638x^42+658x^43+538x^44+434x^45+321x^46+228x^47+175x^48+76x^49+69x^50+20x^51+33x^52+6x^53+6x^54+4x^56+1x^62

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 4.63 seconds.