The generator matrix

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

generates a code of length 50 over Z2[X]/(X^3) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+191x^40+522x^42+16x^43+784x^44+188x^45+1202x^46+636x^47+2013x^48+1180x^49+2738x^50+1244x^51+2228x^52+660x^53+1232x^54+148x^55+715x^56+20x^57+402x^58+4x^59+196x^60+46x^62+15x^64+2x^66+1x^80

The gray image is a linear code over GF(2) with n=200, k=14 and d=80.
This code was found by Heurico 1.16 in 14.2 seconds.