The generator matrix

 1  0  0  1  1  1  1  1  1 2X^2  1  1 2X^2+X  1  1  1  X  1  1 2X^2+X  1  1 X^2+2X  1  1  1  1  0  1  1  1 2X^2+X X^2  1  1 X^2+2X  1  1 2X  1  1 2X^2+2X  1  1  1 2X  1  1 X^2  1  1  1  1  1
 0  1  0 2X^2  1 2X^2+1 2X^2+2  X  2  1 2X^2+2X+1 2X^2+2X+2  1 X^2 2X^2+X+2 X^2+2X+1  1 2X^2+X+1 X^2+X+1  0 X^2+2X+2 2X^2+X  1 2X^2+2X 2X 2X^2+2X+2 X^2+2 2X 2X^2+1 X+1 2X  1  1 X^2+2X+2  2 2X X^2+X+2 X^2+X  1 2X^2+1 X^2+X  1 X^2+2 2X^2+X X^2  1 2X+1 X+2  1 2X+1 2X^2+2X X^2+X+2 X+2 2X^2+2X
 0  0  1 2X^2+2X+1 2X+1 2X^2 X^2+X+2 X+2 X^2+2X 2X^2+1 2X^2+2X+2 2X^2+1 2X^2+2 X^2+X 2X^2+X+2 X^2 X^2+1  1 2X+2  1  X X+1 X^2+X  0 X^2+2 2X^2+X+1  2  1 2X X^2+2X+1 2X+2 2X+2 X^2+X 2X^2+X+2 X^2+X+1  1 2X^2+X+1 X^2+X 2X^2+X+2 X+1 2X^2+2X+1 2X+1 2X^2+2X+2 X^2+2 2X^2+1 2X^2+2X  X  1 X^2+2X+2 2X^2+2 X^2+2X X^2+2X+2 2X+1 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+774x^102+648x^103+1584x^104+2634x^105+1674x^106+1404x^107+3028x^108+1476x^109+1476x^110+1974x^111+774x^112+756x^113+1002x^114+288x^115+126x^116+38x^117+6x^120+18x^123+2x^126

The gray image is a linear code over GF(3) with n=486, k=9 and d=306.
This code was found by Heurico 1.16 in 0.678 seconds.