The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  X  1  1  1  X  1  X  1  1  1  1  1  X  X  1  1  1  1  1  1  X  X
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  0  X  0  X  X  X  0  X  0  X
 0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  0  X  X  X  X  X  X  0  0  X  X  0  0  X  X  X  X
 0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  0  X  0  X  X  X  X  0  0  X  0  X  0  0  0  0  X  X  0  X  0  X
 0  0  0  0  X  0  0  0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  X  0  X  X  0  X  0  X  0  X  X  X  X  X  0  X  0  X  X
 0  0  0  0  0  X  0  0  0  0  0  0  0  0  X  X  X  0  0  X  X  X  X  X  X  0  0  X  0  X  X  X  X  0  0  X  0  0  0  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  X  X  X  X  0  0  0  X  X  X  0  0  0  0  X  X  0  0  0  X  0  0  0  X  X  X  0
 0  0  0  0  0  0  0  X  0  0  0  0  0  X  X  0  X  X  0  X  X  X  0  0  0  X  0  0  X  0  0  X  0  0  0  0  0  X  X  0  0
 0  0  0  0  0  0  0  0  X  0  0  0  0  X  0  0  0  0  0  0  X  X  0  X  X  0  0  0  X  X  X  0  X  X  0  X  X  0  X  X  0
 0  0  0  0  0  0  0  0  0  X  0  0  0  X  0  X  X  0  X  0  0  X  X  0  X  X  0  X  X  X  X  X  0  0  X  0  X  X  0  X  X
 0  0  0  0  0  0  0  0  0  0  X  0  0  X  0  X  X  X  X  X  0  0  0  X  0  0  0  X  0  0  X  0  X  X  0  0  0  X  X  X  X
 0  0  0  0  0  0  0  0  0  0  0  X  0  X  X  0  X  0  X  X  X  0  0  0  X  X  X  0  0  X  0  X  X  0  X  0  0  0  X  X  0
 0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  X  X  0  X  0  X  0  0  0  X  X  0  0  0  X  X  X  0  0  0  0  0  0  0

generates a code of length 41 over Z2[X]/(X^2) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+74x^26+189x^28+284x^30+417x^32+674x^34+1261x^36+2199x^38+3024x^40+3076x^42+2293x^44+1321x^46+680x^48+410x^50+251x^52+121x^54+68x^56+22x^58+6x^60+11x^62+2x^64

The gray image is a linear code over GF(2) with n=82, k=14 and d=26.
This code was found by Heurico 1.16 in 33.5 seconds.