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

generates a code of length 55 over Z3[X]/(X^3) who´s minimum homogenous weight is 97.

Homogenous weight enumerator: w(x)=1x^0+96x^97+138x^99+324x^100+132x^102+450x^103+324x^104+254x^105+1128x^106+1944x^107+572x^108+2646x^109+3888x^110+482x^111+2754x^112+2592x^113+304x^114+768x^115+174x^117+378x^118+22x^120+144x^121+28x^123+60x^124+40x^126+10x^129+8x^132+16x^135+2x^138+4x^144

The gray image is a linear code over GF(3) with n=495, k=9 and d=291.
This code was found by Heurico 1.16 in 40.8 seconds.