The generator matrix

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

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+80x^39+179x^40+336x^41+470x^42+592x^43+801x^44+1040x^45+1332x^46+1640x^47+1837x^48+2026x^49+2245x^50+2330x^51+2481x^52+2496x^53+2416x^54+2274x^55+1997x^56+1628x^57+1309x^58+1020x^59+723x^60+568x^61+361x^62+228x^63+151x^64+90x^65+47x^66+26x^67+19x^68+8x^69+10x^70+2x^71+2x^72+1x^74+1x^78+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 1.16 in 95.7 seconds.