The generator matrix

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

generates a code of length 52 over Z2[X]/(X^2) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+58x^38+342x^40+1042x^42+1718x^44+2572x^46+3661x^48+4272x^50+4976x^52+4626x^54+4030x^56+2668x^58+1563x^60+776x^62+296x^64+96x^66+46x^68+16x^70+6x^72+2x^74+1x^76

The gray image is a linear code over GF(2) with n=104, k=15 and d=38.
This code was found by Heurico 1.16 in 98.3 seconds.