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

generates a code of length 55 over Z2[X]/(X^3) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+24x^50+10x^51+10x^52+34x^53+102x^54+172x^55+78x^56+28x^57+23x^58+10x^59+6x^60+2x^61+10x^62+1x^64+1x^106

The gray image is a linear code over GF(2) with n=220, k=9 and d=100.
This code was found by Heurico 1.16 in 0.0993 seconds.