The generator matrix

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

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+203x^44+132x^45+394x^46+304x^47+506x^48+336x^49+482x^50+320x^51+436x^52+324x^53+308x^54+112x^55+129x^56+8x^57+52x^58+28x^60+10x^62+8x^64+2x^66+1x^68

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 0.787 seconds.