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

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+80x^99+90x^101+300x^102+72x^103+126x^104+580x^105+594x^106+84x^107+2272x^108+1188x^109+36x^110+628x^111+90x^112+60x^113+88x^114+60x^116+120x^117+18x^119+44x^120+12x^122+12x^123+2x^126+2x^132+2x^150

The gray image is a linear code over GF(3) with n=486, k=8 and d=297.
This code was found by Heurico 1.16 in 0.264 seconds.