The generator matrix

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

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+550x^44+1220x^46+1652x^48+1610x^50+1491x^52+976x^54+505x^56+130x^58+55x^60+2x^64

The gray image is a linear code over GF(2) with n=200, k=13 and d=88.
This code was found by Heurico 1.11 in 60.6 seconds.