The generator matrix

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

generates a code of length 41 over Z2[X]/(X^2) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+54x^30+56x^31+150x^32+118x^33+274x^34+308x^35+398x^36+486x^37+494x^38+688x^39+656x^40+764x^41+688x^42+712x^43+548x^44+524x^45+410x^46+248x^47+224x^48+142x^49+106x^50+36x^51+62x^52+14x^53+18x^54+8x^56+4x^58+1x^64

The gray image is a linear code over GF(2) with n=82, k=13 and d=30.
This code was found by Heurico 1.16 in 4.87 seconds.