The generator matrix

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

generates a code of length 57 over Z3[X]/(X^3) who´s minimum homogenous weight is 110.

Homogenous weight enumerator: w(x)=1x^0+72x^110+58x^111+684x^112+360x^113+144x^114+360x^115+144x^116+14x^117+252x^118+72x^119+18x^120+2x^129+6x^132

The gray image is a linear code over GF(3) with n=513, k=7 and d=330.
This code was found by Heurico 1.16 in 0.0666 seconds.