The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  X X^2+X  1 X^2 X^2+X  1 X^2  1 X^2+X X^2+X  1  1 X^2  0  0  1  1  X  1  1  0  1  1  1  1  1 X^2  1 X^2  1  1  1  1 X^2+X  0  1  X  1  1
 0  1  0  0  0  1  1  1 X^2+X+1 X^2+1  X  1 X^2+X X^2  1 X^2 X^2+X  1 X^2+X+1 X^2  X  1  1  1  1  1 X^2+X  X  1 X^2+X+1 X^2+X  X  0 X^2+X X^2  1 X^2+X  1 X^2  0 X^2  X X^2 X^2+X+1 X^2  1 X^2+X+1  1 X^2+X+1  X
 0  0  1  0  1  1  0  1 X^2+1 X^2+X  X X^2+1  1  1  0 X^2  1 X+1 X^2+X+1  1  1  0  0  X X^2+X X^2 X+1 X^2  1 X^2+1 X^2  1 X^2+1 X+1  X X^2+X X^2+X  1 X^2+X  1  X X^2+X  1  X  1 X^2 X^2 X^2  1  0
 0  0  0  1  1  0  1 X^2+1 X^2+X+1 X^2 X^2+X+1  0 X+1 X^2  1  1  1 X+1 X^2+X+1 X^2+1  0 X+1  X X^2+1 X^2 X^2+X  0 X^2 X^2+X X^2+X  X  0 X^2+1  X X^2+X  1 X^2+1 X^2+1  X  X X^2+X+1  1 X^2+X+1  X X+1 X^2  0 X^2+1 X+1  1
 0  0  0  0 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2
 0  0  0  0  0 X^2  0  0  0  0  0  0  0 X^2  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2
 0  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0 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+52x^41+328x^42+592x^43+1088x^44+1446x^45+2065x^46+2566x^47+2930x^48+3468x^49+3429x^50+3690x^51+3214x^52+2604x^53+2070x^54+1346x^55+870x^56+456x^57+282x^58+118x^59+82x^60+38x^61+17x^62+8x^63+7x^64+1x^66

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.