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

generates a code of length 57 over Z3[X]/(X^3) who´s minimum homogenous weight is 104.

Homogenous weight enumerator: w(x)=1x^0+264x^104+238x^105+576x^107+452x^108+1260x^110+1030x^111+1458x^112+2778x^113+3136x^114+2916x^115+2700x^116+1192x^117+492x^119+246x^120+378x^122+130x^123+216x^125+106x^126+66x^128+16x^129+18x^131+6x^132+4x^135+2x^138+2x^156

The gray image is a linear code over GF(3) with n=513, k=9 and d=312.
This code was found by Heurico 1.16 in 1.88 seconds.