The generator matrix

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

generates a code of length 50 over Z2[X]/(X^3) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+74x^44+272x^45+342x^46+524x^47+358x^48+402x^49+376x^50+500x^51+260x^52+272x^53+196x^54+198x^55+128x^56+106x^57+40x^58+24x^59+10x^60+4x^61+6x^62+2x^63+1x^64

The gray image is a linear code over GF(2) with n=200, k=12 and d=88.
This code was found by Heurico 1.16 in 0.465 seconds.