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

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+114x^111+162x^112+36x^113+1524x^114+108x^115+18x^116+6x^117+54x^118+54x^120+36x^122+2x^171

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 0.1 seconds.