The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2 X^2  1  1  1  1  X  1  1  1  0  1  0  1  1  X  X  1  1  X  X  X  0  X  1
 0  X  0  0  0  X X^2+X  X X^2 X^2  X  0  0  X  X X^2+X  0  0 X^2+X  X X^2  X X^2+X  X X^2  X  X  X X^2+X X^2+X X^2 X^2  0 X^2  X  X X^2+X  X X^2+X X^2+X  X  0  0  0 X^2  0 X^2+X  X X^2+X  0
 0  0  X  0  X  X  X  0 X^2  0 X^2+X  X X^2+X  0 X^2+X  0 X^2 X^2+X X^2 X^2+X  0 X^2  X  0 X^2+X X^2 X^2+X  0  X X^2+X  X X^2+X X^2 X^2+X  0 X^2+X X^2+X  0  0 X^2+X X^2 X^2+X X^2 X^2+X X^2 X^2  X X^2 X^2+X X^2+X
 0  0  0  X  X  0  X X^2+X  0  X X^2  X X^2 X^2+X  X  0 X^2  X  X  0 X^2+X X^2 X^2+X X^2+X  0 X^2+X  0  0  X  0 X^2 X^2+X X^2 X^2 X^2  X  X X^2  0 X^2 X^2+X X^2  X X^2+X  X  X X^2+X  0 X^2+X X^2+X
 0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2
 0  0  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0  0  0 X^2 X^2  0 X^2  0  0  0  0  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+247x^44+48x^45+176x^47+305x^48+288x^49+288x^51+232x^52+176x^53+48x^55+190x^56+40x^60+8x^64+1x^76

The gray image is a linear code over GF(2) with n=200, k=11 and d=88.
This code was found by Heurico 1.16 in 14.3 seconds.