The generator matrix

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

generates a code of length 41 over Z2[X]/(X^2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+92x^28+36x^30+370x^32+272x^34+950x^36+940x^38+1503x^40+1136x^42+1406x^44+556x^46+591x^48+128x^50+170x^52+4x^54+29x^56+6x^60+2x^64

The gray image is a linear code over GF(2) with n=82, k=13 and d=28.
This code was found by Heurico 1.16 in 5.13 seconds.