The generator matrix

 1  0  1  1  1 X^2  1  1  0  0  1  1  1  0  1  1  1  0  1  1  0  1  1 X^2  1  1 X^2+X  1  1  1  X  0  1  1  1  1  X  1  X  1  1  X  1  1  0 X^2  1  1  1  1  1  X X^2  X  1
 0  1  1  0  1  1 X^2 X+1  1  1 X^2 X^2+X+1 X^2  1 X^2+1 X+1 X^2  1  X X+1  1  0  1  1 X^2+X X^2+X+1  1 X+1 X^2+1  0  1  1 X+1 X+1 X+1 X^2+X+1  1 X^2+X+1  1 X^2 X^2+X  0 X^2+X X^2+X  1  1  1 X^2+X+1 X^2  0  1  1  1 X^2+X  0
 0  0  X  0  0  0  0 X^2 X^2+X  X X^2+X X^2+X X^2+X X^2  0  X X^2+X  X  X  0  0 X^2 X^2+X  X X^2+X  X X^2 X^2 X^2 X^2+X  0  X X^2 X^2+X X^2  X X^2+X X^2  X  0  0 X^2 X^2 X^2+X X^2  0 X^2  0  X  X  X X^2+X X^2  X  0
 0  0  0  X  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2+X  X  X  X X^2+X  X X^2+X  X X^2+X X^2+X X^2+X X^2 X^2  0 X^2  X  X  0  X  X  X X^2  X  0  0  0  X  X  X  0  0 X^2 X^2+X  0  X  X X^2+X X^2 X^2 X^2 X^2+X  0
 0  0  0  0  X X^2+X X^2+X X^2  X  0  0 X^2+X  X  X  X  X X^2  0 X^2+X  0 X^2 X^2+X X^2 X^2 X^2  0 X^2  0  0 X^2+X X^2+X X^2+X  X  X  X X^2  X  0 X^2+X X^2 X^2+X  0 X^2  0  X  0  0  X  X X^2+X  0 X^2+X X^2  X 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+77x^48+76x^49+344x^50+236x^51+419x^52+320x^53+522x^54+288x^55+439x^56+300x^57+376x^58+236x^59+218x^60+72x^61+84x^62+8x^63+46x^64+16x^66+11x^68+2x^70+5x^72

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 0.728 seconds.