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

generates a code of length 51 over Z3[X]/(X^3) who´s minimum homogenous weight is 93.

Homogenous weight enumerator: w(x)=1x^0+78x^93+54x^94+246x^96+114x^97+216x^98+258x^99+1080x^100+864x^101+198x^102+1998x^103+864x^104+134x^105+66x^106+142x^108+30x^109+80x^111+36x^112+52x^114+18x^115+22x^117+6x^118+2x^120+2x^147

The gray image is a linear code over GF(3) with n=459, k=8 and d=279.
This code was found by Heurico 1.16 in 0.24 seconds.