The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  1 X^2+X  1  1 X^2+X  1  1  0  1  0  1  1  1 X^2+X  1  1  1  0  1  1  1  1  1 X^2+X  0 X^2+X  1  1  1  1  1  1 X^2 X^2  1  1  0  1 X^2+X  X X^2+X  1  1  X  1
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+X X^2+1  1  0 X+1  1 X^2+X X^2+1  1 X^2+1  1  0 X^2+X X+1  1 X^2+X  0 X+1  1  0 X^2+X  X X^2 X^2+X  1  1  1 X^2+X  0 X+1 X^2+X+1 X^2+1 X^2+1  1  1  1 X^2+X+1  1 X^2+1  1  1  1  X  0  1 X+1
 0  0 X^2  0  0  0  0  0  0  0  0 X^2  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  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2
 0  0  0 X^2  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0  0  0  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0
 0  0  0  0 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0  0  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0  0 X^2  0  0
 0  0  0  0  0 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2
 0  0  0  0  0  0 X^2  0 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2
 0  0  0  0  0  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  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 48.

Homogenous weight enumerator: w(x)=1x^0+123x^48+72x^49+298x^50+208x^51+408x^52+312x^53+458x^54+352x^55+505x^56+312x^57+334x^58+208x^59+329x^60+72x^61+62x^62+22x^64+12x^68+5x^72+3x^76

The gray image is a linear code over GF(2) with n=220, k=12 and d=96.
This code was found by Heurico 1.16 in 1.71 seconds.