The generator matrix

 1  0  0  0  0  0  1  1  1  X  1  1  X  X  X  1  1  0  1  1  1  X  1  X  1  0  1  X  1  X  1  1  1  0  1  1  1  X  1  1
 0  1  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  1  1 X+1  1  1  1 X+1  1 X+1  1 X+1  1  X  0 X+1  X  0  1  0  X  1  0
 0  0  1  0  0  0  0  0  0  0  1  1  1  0  1 X+1  1  1  X  0  0  X  1 X+1  X  0  X  1 X+1 X+1  X X+1  X  1  X  X  1  1 X+1  0
 0  0  0  1  0  0  0  1  1  1  1 X+1  0  1  0  X  1 X+1  X  X X+1  X  0  X  1 X+1  X  1  0  1  0 X+1 X+1  1  1  1  0 X+1  0  0
 0  0  0  0  1  0  1  1  X X+1  0 X+1  1 X+1  X  1  X  X X+1  0 X+1 X+1  0  0  1  X X+1  X  X  1  X X+1  1  1  X X+1  X X+1 X+1  0
 0  0  0  0  0  1  1  X X+1  1  0  1  1  0 X+1  X  1  0  0  0 X+1  1  X  1  0 X+1  X  0  1  0  X  0  X  X  0 X+1  0  1 X+1  0
 0  0  0  0  0  0  X  0  X  0  X  0  0  X  X  X  0  0  0  X  0  X  0  0  X  X  X  0  0  X  X  X  X  0  0  X  0  0  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+61x^30+82x^31+211x^32+298x^33+351x^34+434x^35+476x^36+536x^37+614x^38+660x^39+659x^40+718x^41+648x^42+634x^43+460x^44+410x^45+375x^46+208x^47+150x^48+80x^49+57x^50+28x^51+24x^52+6x^53+6x^54+2x^55+3x^56

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.