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

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+184x^40+550x^42+20x^43+785x^44+92x^45+1268x^46+612x^47+1975x^48+1356x^49+2662x^50+1276x^51+2131x^52+596x^53+1328x^54+140x^55+736x^56+4x^57+418x^58+187x^60+44x^62+15x^64+2x^66+1x^68+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 14.4 seconds.