The generator matrix

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

generates a code of length 50 over Z2[X]/(X^2) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+72x^38+116x^39+228x^40+322x^41+470x^42+568x^43+647x^44+818x^45+860x^46+1004x^47+1107x^48+1200x^49+1286x^50+1258x^51+1238x^52+1140x^53+966x^54+876x^55+667x^56+514x^57+363x^58+236x^59+183x^60+90x^61+60x^62+36x^63+20x^64+12x^65+16x^66+2x^67+4x^68+2x^70+1x^72+1x^74

The gray image is a linear code over GF(2) with n=100, k=14 and d=38.
This code was found by Heurico 1.16 in 48.1 seconds.