The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+2x^54+20x^55+2x^56+4x^57+1x^58+1x^60+1x^62

The gray image is a linear code over GF(2) with n=216, k=5 and d=108.
This code was found by Heurico 1.16 in 0.055 seconds.