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

generates a code of length 59 over Z3[X]/(X^3) who´s minimum homogenous weight is 115.

Homogenous weight enumerator: w(x)=1x^0+402x^115+408x^116+8x^117+726x^118+198x^119+10x^120+150x^121+144x^122+2x^123+126x^124+6x^125+2x^129+2x^132+2x^141

The gray image is a linear code over GF(3) with n=531, k=7 and d=345.
This code was found by Heurico 1.16 in 24.3 seconds.