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

generates a code of length 54 over Z3[X]/(X^3) who´s minimum homogenous weight is 105.

Homogenous weight enumerator: w(x)=1x^0+164x^105+18x^106+36x^107+342x^108+36x^109+18x^110+54x^111+56x^114+2x^132+2x^135

The gray image is a linear code over GF(3) with n=486, k=6 and d=315.
This code was found by Heurico 1.16 in 0.0601 seconds.