The generator matrix

 1  0  0  0  1  1  1 X^2  1  1  1  X  X  1  X  1 X^2  1  1  1  0  1 X^2 X^2  1 X^2+X  1  1  1  X  X  1  X X^2  0 X^2+X  1  1  1  0  1  1  X X^2 X^2+X  1  1 X^2  1  1 X^2  1  1  1  1
 0  1  0  0  X X^2 X^2+X  1 X+1 X^2+1  1  X  1  1  1 X^2+X  1 X^2+X+1  0 X+1 X^2 X+1 X^2  1 X^2+X+1 X^2 X^2+X  X  0 X^2+X  1  1  0  1  1  1 X^2+1 X^2  X  1 X^2+X X^2  1  1  1 X^2 X^2+X+1 X^2+X X^2+X  0  1  0  X X^2+X X^2
 0  0  1  0  X X^2+1  1 X^2+1  0 X^2+1 X^2  1 X+1 X+1  X  0 X^2+X+1 X^2+X+1  1 X^2+X  1 X^2+X+1  X X^2+X  X  1  X  1 X^2+X+1  1 X^2+1 X^2+X X^2  0 X^2+X+1 X^2+1 X+1  0  0 X^2+1 X^2+X+1  1 X^2+X+1 X^2+1 X^2 X^2+X X+1  1  0 X^2+X X^2  0  0 X^2 X^2+X
 0  0  0  1 X+1  1  X X^2+1 X^2+X X^2+X+1 X^2+X+1 X+1  0 X^2+X X^2+1 X^2 X^2+X  1 X^2+X+1  0  X X^2  1 X^2+X+1  1 X+1  X  0 X+1 X^2+X  1 X^2+1  1 X^2  0 X^2 X^2+X X+1 X^2+1 X^2+X+1  0  1  X  0  X X^2 X^2+X X^2 X^2+X  0 X^2+X+1 X^2+1 X^2+X+1 X+1 X^2
 0  0  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0 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+113x^48+266x^49+553x^50+626x^51+754x^52+688x^53+869x^54+818x^55+778x^56+606x^57+606x^58+500x^59+438x^60+244x^61+144x^62+66x^63+72x^64+20x^65+15x^66+6x^67+4x^68+3x^70+2x^74

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 2.21 seconds.