The generator matrix

 1  0  0  1  1  1 X^2+X  1  1  1  1 X^2  X X^2  1  X  1  1  1  0  X  1 X^2+X  1  0  0  1  1  0  1  1  0 X^2  0  1  1  1  0  1 X^2+X  0 X^2  1  1  1  1  1  1  1  0
 0  1  0  0  1  1  1  X  1 X^2 X^2+1  1  X  1  X  1 X^2+1 X^2+X  1  1  0  1  1  X  0  1 X^2+X+1 X^2  1  1 X+1  1  1 X^2+X  0  X  1  X X^2+1  1  1  1 X^2+1 X^2+X+1 X^2  1 X^2+1 X^2+X+1 X^2  1
 0  0  1  1  1  0  1 X+1  1  0 X^2  1  1  0 X^2+X+1  X X+1  0 X^2+X  1  1  1 X^2+1  1  1  X X^2 X^2+X X^2+X X^2+X+1  0  X X^2+X  1 X^2+1 X^2+X+1  X  1  1 X^2  1  X X+1 X^2 X^2  0  1  0 X+1 X^2+X
 0  0  0  X  0  0  0  0  0  0  0  0  0 X^2  0  0  X X^2+X X^2+X X^2+X X^2+X X^2+X  X  X  X X^2  X  X X^2  X X^2 X^2  X X^2+X X^2+X X^2+X  X  0 X^2  X X^2+X X^2 X^2  0 X^2+X X^2 X^2 X^2  X X^2+X
 0  0  0  0  X  0  0  0 X^2 X^2+X  X  X  X X^2+X  X  0  0 X^2 X^2+X X^2  X X^2+X X^2+X X^2+X  0 X^2+X  0  X X^2 X^2  0  X X^2  0  0  X  X X^2+X X^2+X X^2 X^2 X^2+X X^2  X  X  X  X X^2  X  0
 0  0  0  0  0  X X^2+X X^2+X  0  0  X X^2+X X^2  0 X^2+X X^2 X^2+X X^2+X X^2 X^2 X^2+X  X X^2  0 X^2+X  0  0  X X^2 X^2  0 X^2+X  0 X^2  X  X X^2+X X^2+X  0  X  X X^2+X X^2+X  X X^2+X X^2  X X^2+X X^2 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+160x^41+322x^42+572x^43+931x^44+1428x^45+1951x^46+2524x^47+3118x^48+3476x^49+3778x^50+3556x^51+3153x^52+2548x^53+1911x^54+1448x^55+865x^56+480x^57+248x^58+152x^59+84x^60+32x^61+13x^62+4x^63+8x^64+4x^65+1x^70

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 60.5 seconds.