The generator matrix

 1  0  0  0  1  1  1  0  1  X  1 X^2+X  1 X^2+X  1  1  1  0  1  X X^2  0 X^2+X  1  X  1  1 X^2  0  1  1  X  1  1 X^2+X X^2+X  1  1  1  1  1  1  1  0 X^2+X  0  1  1  X  1
 0  1  0  0  0  1  1  1 X^2 X^2+X X^2+1  1 X^2  1  1 X^2+X X^2+X+1  1 X+1  X  1  1  X X^2+X X^2 X^2+X+1 X^2+1  1  1  0 X^2+1  1 X+1 X^2  1  1 X^2+X  X  X X^2+X+1  1 X^2+X X^2+X  0  1  X  X X+1  X  0
 0  0  1  0  1  1 X^2 X^2+1 X^2+X+1  1  1 X^2+X+1  X  X X^2 X^2+X+1 X^2  1 X+1 X^2+X  X  0  1  0  1 X+1 X^2 X^2+X+1  X  0 X^2+X+1 X^2+1 X^2+1  1  X X^2+1 X+1  0 X^2  0 X^2+X X^2+X  1  1 X^2+X+1  1 X^2  X  1  0
 0  0  0  1  1  0 X^2+1  1 X^2  1 X^2+1 X^2  1 X^2+X+1  0  1  1 X^2+X+1 X^2+X+1  1 X^2+X+1  X X+1 X^2+X+1  X X^2 X^2+1 X^2 X^2+X  X X+1 X^2 X^2+1 X^2+X  1 X^2+1 X^2+X X^2+X X+1  X X^2  X  1  X X+1 X^2  1 X^2 X^2 X^2
 0  0  0  0  X  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2+X  X X^2+X X^2+X  X X^2+X  X X^2+X X^2+X X^2+X X^2+X  X  X  X X^2  X X^2  0 X^2+X  X X^2+X  0 X^2+X  X  X  0  X  0
 0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0  0  0

generates a code of length 50 over Z2[X]/(X^3) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+60x^41+307x^42+566x^43+1162x^44+1406x^45+2129x^46+2506x^47+3078x^48+3064x^49+3814x^50+3424x^51+3425x^52+2402x^53+2278x^54+1278x^55+875x^56+466x^57+257x^58+144x^59+61x^60+24x^61+13x^62+16x^63+6x^64+2x^65+2x^66+2x^67

The gray image is a linear code over GF(2) with n=200, k=15 and d=82.
This code was found by Heurico 1.16 in 29.1 seconds.