The generator matrix

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

generates a code of length 52 over Z2[X]/(X^2) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+54x^39+153x^40+308x^41+520x^42+678x^43+811x^44+1114x^45+1294x^46+1502x^47+1827x^48+2078x^49+2258x^50+2314x^51+2497x^52+2440x^53+2388x^54+2268x^55+1974x^56+1748x^57+1330x^58+978x^59+767x^60+534x^61+332x^62+238x^63+145x^64+90x^65+60x^66+30x^67+13x^68+8x^69+10x^70+2x^71+3x^72+1x^80

The gray image is a linear code over GF(2) with n=104, k=15 and d=39.
This code was found by Heurico 1.11 in 38.8 seconds.