The generator matrix

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

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+154x^90+102x^91+66x^92+360x^93+498x^94+588x^95+1188x^96+3630x^97+1554x^98+3428x^99+8820x^100+3330x^101+6098x^102+12258x^103+3132x^104+4310x^105+6300x^106+1416x^107+834x^108+420x^109+114x^110+208x^111+42x^112+6x^113+104x^114+6x^115+32x^117+22x^120+14x^123+4x^126+8x^129+2x^135

The gray image is a linear code over GF(3) with n=459, k=10 and d=270.
This code was found by Heurico 1.16 in 7.41 seconds.