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

generates a code of length 57 over Z3[X]/(X^3) who´s minimum homogenous weight is 102.

Homogenous weight enumerator: w(x)=1x^0+114x^102+96x^103+90x^104+300x^105+210x^106+186x^107+616x^108+660x^109+690x^110+1548x^111+1464x^112+2184x^113+2642x^114+1992x^115+2280x^116+2082x^117+1146x^118+228x^119+418x^120+114x^121+156x^122+156x^123+120x^124+18x^125+56x^126+30x^127+22x^129+30x^132+18x^135+4x^138+4x^141+8x^144

The gray image is a linear code over GF(3) with n=513, k=9 and d=306.
This code was found by Heurico 1.16 in 2 seconds.