The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  1  X  X  1  1  X  0  X  0  X  1  0  0  1  X  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  X  0  X  X  X  0  X  0  X  0  X  0  X  X  0  X  X  0  0  0  0  X  0  0  0  X  0  X
 0  0  X  0  0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  X  X  0  0  0  0  0  X  X  X  X  X  0  X  0  0  0  X  0  X  0  X  X  X  0  0  X  X  X  0  X  0  0  X
 0  0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  X  0  X  X  X  0  X  X  X  0  X  0  0  X  X  X  X  X  X  X  0  0  X  0  0  X  0  0  X  0  0  X  0  0  X  0  X
 0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  0  X  X  X  0  X  X  X  0  0  0  0  0  X  0  0  0  X  0  0  X  0  X  X  0  X  0  X  X  X  0  0  0  0  0  X  X  0
 0  0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  X  X  0  0  X  0  0  X  X  0  0  0  X  X  0  0  0  X  X  0  X  0  X  0  X  0  0  X  0  X  0  0  X  0  X  X
 0  0  0  0  0  0  X  0  0  0  X  0  0  0  X  X  0  0  X  0  0  X  X  0  X  0  X  0  X  0  X  0  X  X  X  0  X  0  X  X  X  0  X  0  0  X  X  X  X  0  X  X  0
 0  0  0  0  0  0  0  X  0  0  X  0  0  X  0  0  X  0  0  X  0  X  X  0  0  X  X  X  0  0  X  X  0  X  X  X  0  0  0  X  X  0  0  X  0  0  X  X  X  X  X  0  X
 0  0  0  0  0  0  0  0  X  0  X  X  X  X  0  0  0  0  X  0  0  0  X  X  X  X  0  0  0  X  0  X  0  0  X  X  X  0  X  0  X  0  X  X  0  0  0  X  0  X  X  X  0
 0  0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  X  X  X  0  X  0  X  0  X  0  X  X  0  0  X  X  X  X  X  X  X  0  0  X  0  X  X  X  X  X  X  X  0  X  X  0

generates a code of length 53 over Z2[X]/(X^2) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+60x^42+116x^44+134x^46+184x^48+273x^50+300x^52+255x^54+245x^56+182x^58+113x^60+84x^62+49x^64+29x^66+14x^68+7x^70+1x^72+1x^76

The gray image is a linear code over GF(2) with n=106, k=11 and d=42.
This code was found by Heurico 1.16 in 1.84 seconds.