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  0  0  X  X X^2  0  1  0  0  1  1 X^2  1  1  1  0
 0  X  0  0  0  0  0  0 X^2 X^2  X X^2+X  X  0  0 X^2 X^2+X X^2+X  X  X  X  0  X  X X^2 X^2+X  X X^2+X X^2 X^2+X  X X^2 X^2  X  0  0  0 X^2+X  0  X X^2+X  X X^2  0 X^2  0 X^2  X  X X^2
 0  0  X  0  0  0  0  0  0  0  0  0 X^2 X^2+X X^2+X X^2+X  X X^2+X X^2+X  X X^2 X^2+X  X X^2  X  X  X X^2  X  X  0  X X^2  0  X X^2  X X^2+X  X X^2  X X^2  X X^2 X^2+X  0  X X^2+X  0  X
 0  0  0  X  0  0 X^2 X^2+X  X  X  X  X X^2 X^2+X  X X^2 X^2  0 X^2 X^2 X^2 X^2  X X^2+X X^2  X X^2+X  X  X X^2+X X^2  X  X  0  X X^2 X^2  0 X^2  0 X^2+X  X X^2 X^2  0  0 X^2+X  0 X^2  0
 0  0  0  0  X  0 X^2+X X^2+X  X X^2 X^2+X X^2+X  0  X  X  0 X^2  X  0 X^2+X X^2+X X^2+X  X  0 X^2+X X^2+X X^2  0  0 X^2  X X^2 X^2+X  0 X^2 X^2  0  X  X X^2 X^2+X X^2  X  0 X^2 X^2  0 X^2  0  0
 0  0  0  0  0  X  X X^2 X^2+X  X X^2+X X^2  X  X  0  X  0 X^2+X X^2+X  0  X X^2 X^2+X  X  X X^2  0  0 X^2  X X^2 X^2+X  0 X^2  X  X X^2+X X^2  0  0 X^2 X^2+X X^2+X  0 X^2  X  X X^2 X^2  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+76x^41+153x^42+210x^43+254x^44+258x^45+392x^46+598x^47+740x^48+986x^49+996x^50+850x^51+798x^52+536x^53+406x^54+310x^55+204x^56+160x^57+91x^58+76x^59+44x^60+30x^61+10x^62+4x^63+6x^64+2x^65+1x^80

The gray image is a linear code over GF(2) with n=200, k=13 and d=82.
This code was found by Heurico 1.16 in 3.82 seconds.