The generator matrix

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

generates a code of length 51 over Z2[X]/(X^2) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+73x^38+158x^39+315x^40+426x^41+660x^42+758x^43+1119x^44+1270x^45+1549x^46+1812x^47+2110x^48+2358x^49+2210x^50+2632x^51+2535x^52+2514x^53+2111x^54+1946x^55+1726x^56+1282x^57+1026x^58+746x^59+541x^60+294x^61+263x^62+132x^63+85x^64+46x^65+38x^66+8x^67+13x^68+2x^69+4x^70+3x^72+2x^74

The gray image is a linear code over GF(2) with n=102, k=15 and d=38.
This code was found by Heurico 1.16 in 96.8 seconds.