The generator matrix

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

generates a code of length 53 over Z2[X]/(X^2) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+74x^39+217x^40+396x^41+648x^42+906x^43+1258x^44+1646x^45+1997x^46+2554x^47+3068x^48+3594x^49+4150x^50+4586x^51+4843x^52+5046x^53+5035x^54+4702x^55+4428x^56+3806x^57+3254x^58+2666x^59+2013x^60+1534x^61+1059x^62+778x^63+471x^64+314x^65+218x^66+114x^67+77x^68+46x^69+21x^70+4x^71+7x^72+2x^73+2x^74+1x^76

The gray image is a linear code over GF(2) with n=106, k=16 and d=39.
This code was found by Heurico 1.11 in 190 seconds.