The generator matrix

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

generates a code of length 54 over Z3[X]/(X^3) who´s minimum homogenous weight is 102.

Homogenous weight enumerator: w(x)=1x^0+268x^102+252x^103+288x^104+1100x^105+540x^106+216x^107+982x^108+756x^109+324x^110+994x^111+396x^112+144x^113+268x^114+10x^117+14x^120+6x^126+2x^138

The gray image is a linear code over GF(3) with n=486, k=8 and d=306.
This code was found by Heurico 1.16 in 0.144 seconds.