The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 X 1 1 1 1 X X 1 1 1 X X X 1 X X^2 X^2 0 X X X X X X 1
0 X^2 2X^2 0 X^2 2X^2 0 X^2 2X^2 0 X^2 2X^2 0 X^2 2X^2 0 X^2 2X^2 0 X^2 2X^2 0 X^2 2X^2 0 X^2 2X^2 X^2 0 2X^2 X^2 2X^2 0 X^2 X^2 2X^2 2X^2 0 X^2 0 X^2 2X^2 2X^2 0 X^2 2X^2 X^2 0 X^2 2X^2 0 X^2 0 0
generates a code of length 54 over Z3[X]/(X^3) who´s minimum homogenous weight is 108.
Homogenous weight enumerator: w(x)=1x^0+56x^108+6x^110+6x^111+6x^113+6x^116
The gray image is a linear code over GF(3) with n=486, k=4 and d=324.
This code was found by Heurico 1.16 in 0.0423 seconds.