The generator matrix

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

generates a code of length 57 over Z3[X]/(X^3) who´s minimum homogenous weight is 111.

Homogenous weight enumerator: w(x)=1x^0+272x^111+582x^112+578x^114+348x^115+120x^117+204x^118+76x^120+2x^123+2x^135+2x^141

The gray image is a linear code over GF(3) with n=513, k=7 and d=333.
This code was found by Heurico 1.16 in 4.99 seconds.