The generator matrix

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

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+55x^38+170x^39+322x^40+426x^41+627x^42+888x^43+1055x^44+1250x^45+1607x^46+1736x^47+2089x^48+2372x^49+2323x^50+2486x^51+2450x^52+2478x^53+2257x^54+2024x^55+1628x^56+1278x^57+1063x^58+744x^59+576x^60+330x^61+229x^62+132x^63+64x^64+52x^65+26x^66+10x^67+6x^68+6x^69+4x^70+2x^71+1x^76+1x^82

The gray image is a linear code over GF(2) with n=102, k=15 and d=38.
This code was found by Heurico 1.11 in 37.4 seconds.