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

generates a code of length 51 over Z3[X]/(X^3) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+134x^90+24x^91+78x^92+252x^93+330x^94+192x^95+422x^96+534x^97+216x^98+598x^99+4122x^100+276x^101+806x^102+8424x^103+264x^104+762x^105+924x^106+270x^107+340x^108+174x^109+132x^110+160x^111+48x^112+30x^113+100x^114+26x^117+22x^120+8x^123+6x^126+2x^129+4x^132+2x^135

The gray image is a linear code over GF(3) with n=459, k=9 and d=270.
This code was found by Heurico 1.16 in 1.77 seconds.