The generator matrix

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

generates a code of length 54 over Z3[X]/(X^3) who´s minimum homogenous weight is 99.

Homogenous weight enumerator: w(x)=1x^0+606x^99+252x^100+612x^101+2442x^102+2448x^103+2844x^104+4704x^105+4626x^106+5868x^107+6858x^108+7902x^109+6462x^110+5730x^111+3492x^112+1692x^113+1470x^114+234x^115+18x^116+472x^117+234x^120+72x^123+10x^126

The gray image is a linear code over GF(3) with n=486, k=10 and d=297.
This code was found by Heurico 1.16 in 13.9 seconds.