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

generates a code of length 55 over Z2[X]/(X^3) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+43x^48+88x^49+98x^50+104x^51+183x^52+258x^53+223x^54+218x^55+191x^56+166x^57+149x^58+94x^59+62x^60+46x^61+33x^62+22x^63+24x^64+18x^65+9x^66+10x^67+7x^68+1x^88

The gray image is a linear code over GF(2) with n=220, k=11 and d=96.
This code was found by Heurico 1.16 in 0.296 seconds.