The generator matrix

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

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+164x^28+40x^30+632x^32+474x^34+1756x^36+1870x^38+3453x^40+2532x^42+2782x^44+1060x^46+1138x^48+162x^50+248x^52+6x^54+54x^56+10x^60+1x^64+1x^72

The gray image is a linear code over GF(2) with n=82, k=14 and d=28.
This code was found by Heurico 1.16 in 20.3 seconds.