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

generates a code of length 57 over Z3[X]/(X^3) who´s minimum homogenous weight is 105.

Homogenous weight enumerator: w(x)=1x^0+618x^105+18x^107+1274x^108+54x^109+684x^110+1716x^111+972x^112+2538x^113+4002x^114+1782x^115+2520x^116+1818x^117+108x^118+72x^119+654x^120+510x^123+226x^126+114x^129+2x^153

The gray image is a linear code over GF(3) with n=513, k=9 and d=315.
This code was found by Heurico 1.16 in 7.48 seconds.