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

generates a code of length 55 over Z2[X]/(X^3) who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+76x^47+132x^48+138x^49+207x^50+270x^51+304x^52+330x^53+422x^54+440x^55+394x^56+364x^57+284x^58+232x^59+148x^60+100x^61+80x^62+56x^63+39x^64+26x^65+28x^66+10x^67+4x^68+2x^69+2x^70+4x^71+2x^72+1x^82

The gray image is a linear code over GF(2) with n=220, k=12 and d=94.
This code was found by Heurico 1.16 in 3.62 seconds.