The generator matrix

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

generates a code of length 53 over Z2[X]/(X^2) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+78x^41+177x^42+240x^43+356x^44+396x^45+555x^46+664x^47+815x^48+962x^49+1056x^50+1144x^51+1158x^52+1224x^53+1128x^54+1108x^55+1078x^56+974x^57+810x^58+756x^59+537x^60+376x^61+324x^62+164x^63+134x^64+82x^65+36x^66+20x^67+12x^68+4x^69+8x^70+4x^72+1x^74+1x^76+1x^78

The gray image is a linear code over GF(2) with n=106, k=14 and d=41.
This code was found by Heurico 1.16 in 53.7 seconds.