The generator matrix

 1  0  0  1  1  1  X  0  1  1  1  1  X X^2  1  1 X^2+X  1  1 X^2+X  X  X  1  1  1  1 X^2  X  1  0  1  1  1 X^2+X  1  X  1 X^2 X^2+X  X  1  1  1  X  1  X X^2+X X^2+X  1  1 X^2+X X^2+X  X  1  1
 0  1  0  0  1 X^2+X+1  1  1  X  X X+1 X+1 X^2+X  1 X^2+1  X  1 X^2+X+1  0 X^2 X^2+X  1 X^2+X+1  1 X^2+X X^2+1  1  1 X^2  1 X^2+X X+1 X+1  0  1  1  0  1  1  1  1 X^2+X X^2  1 X^2+X  1  1  1 X^2+1  0  X X^2+X  1  X  0
 0  0  1  1  1  0  1 X+1 X+1  X X^2+X+1  X  1  X  1 X^2  1  0 X+1  1  1  X X^2+1 X^2 X+1 X+1 X^2+1  0 X^2+X  0 X^2+X  X X^2+X+1  1 X^2  1 X^2+1 X^2+1  X X^2+X+1  0 X^2+1  X  X X^2+X+1 X+1 X^2+1  0 X^2+X+1  X  1  1 X^2  1 X^2+1
 0  0  0  X  0 X^2+X X^2  0  X X^2 X^2  X  0  0 X^2+X X^2+X  X  0  0 X^2+X  X X^2+X  X  0 X^2 X^2+X  X X^2 X^2  X  X  0  0 X^2 X^2+X X^2 X^2 X^2+X  X  X X^2  X X^2+X  0 X^2  X X^2+X  0  0 X^2+X X^2  0 X^2+X  X  0
 0  0  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0  0  0  0  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2  0  0
 0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  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+185x^48+184x^49+604x^50+484x^51+895x^52+580x^53+988x^54+652x^55+906x^56+532x^57+788x^58+412x^59+430x^60+172x^61+212x^62+52x^63+60x^64+4x^65+32x^66+19x^68

The gray image is a linear code over GF(2) with n=220, k=13 and d=96.
This code was found by Heurico 1.16 in 2.96 seconds.