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

generates a code of length 57 over Z3[X]/(X^3) who´s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+602x^108+270x^110+720x^111+324x^112+1080x^113+804x^114+648x^115+1080x^116+576x^117+144x^120+186x^123+106x^126+18x^129+2x^153

The gray image is a linear code over GF(3) with n=513, k=8 and d=324.
This code was found by Heurico 1.16 in 48.2 seconds.