The generator matrix

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

generates a code of length 54 over Z2[X]/(X^3) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+62x^51+106x^52+102x^53+90x^54+46x^55+26x^56+10x^57+5x^58+20x^59+25x^60+16x^61+1x^66+1x^68+1x^72

The gray image is a linear code over GF(2) with n=216, k=9 and d=102.
This code was found by Heurico 1.11 in 0.047 seconds.