The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  1 X^2+X  0  1  1  1 X^2+X  1  1 X^2+X  1  0  1 X^2  1  1  1  1  1  1 X^2+X  1  1  1 X^2+X  1  1  1  1  X  1  1  1  0  0  0 X^2  1  1  1
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+X X^2+1  1  1  0 X+1 X^2+1  1 X^2+X X^2+1  1 X+1  1  0  1  X X^2+1  0 X^2+X X^2+X X^2  1 X^2+X X+1 X^2+X+1  1 X+1 X^2+X+1 X^2+1  X  1 X^2+1  1 X^2+X+1  1  1  1  1 X+1 X+1 X+1
 0  0 X^2  0  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0  0 X^2  0  0
 0  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0
 0  0  0  0 X^2  0  0  0 X^2  0 X^2  0 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0
 0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2  0  0  0 X^2
 0  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  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+79x^44+48x^45+288x^46+80x^47+224x^48+128x^49+384x^50+128x^51+196x^52+80x^53+288x^54+48x^55+57x^56+11x^60+5x^64+2x^68+1x^72

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 0.205 seconds.