The generator matrix

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

generates a code of length 54 over Z2[X]/(X^2) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+98x^41+200x^42+334x^43+550x^44+624x^45+873x^46+1014x^47+1310x^48+1556x^49+1741x^50+2072x^51+2217x^52+2472x^53+2433x^54+2478x^55+2336x^56+2092x^57+1929x^58+1604x^59+1293x^60+1058x^61+848x^62+600x^63+413x^64+262x^65+151x^66+78x^67+67x^68+30x^69+13x^70+12x^71+4x^72+3x^74+1x^76+1x^78

The gray image is a linear code over GF(2) with n=108, k=15 and d=41.
This code was found by Heurico 1.11 in 43.3 seconds.