The generator matrix

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

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+252x^41+632x^42+1258x^43+1977x^44+3010x^45+3935x^46+4932x^47+6079x^48+6776x^49+7246x^50+7108x^51+6582x^52+5174x^53+3936x^54+2764x^55+1702x^56+1178x^57+546x^58+250x^59+105x^60+56x^61+25x^62+8x^63+2x^64+2x^65

The gray image is a linear code over GF(2) with n=200, k=16 and d=82.
This code was found by Heurico 1.13 in 37 seconds.