The generator matrix

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

generates a code of length 54 over Z2[X]/(X^3) who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+112x^47+329x^48+416x^49+660x^50+736x^51+896x^52+680x^53+808x^54+736x^55+702x^56+632x^57+530x^58+348x^59+292x^60+128x^61+92x^62+48x^63+32x^64+6x^66+4x^67+4x^68

The gray image is a linear code over GF(2) with n=216, k=13 and d=94.
This code was found by Heurico 1.16 in 2.2 seconds.