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

generates a code of length 50 over Z2[X]/(X^2) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+38x^37+148x^38+300x^39+478x^40+612x^41+858x^42+1006x^43+1289x^44+1584x^45+1747x^46+2104x^47+2202x^48+2408x^49+2662x^50+2510x^51+2503x^52+2382x^53+1907x^54+1662x^55+1310x^56+940x^57+703x^58+530x^59+355x^60+204x^61+146x^62+76x^63+41x^64+24x^65+16x^66+2x^67+13x^68+3x^70+2x^71+1x^74+1x^78

The gray image is a linear code over GF(2) with n=100, k=15 and d=37.
This code was found by Heurico 1.16 in 92.7 seconds.