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

generates a code of length 59 over Z3[X]/(X^3) who´s minimum homogenous weight is 114.

Homogenous weight enumerator: w(x)=1x^0+132x^114+54x^115+228x^116+136x^117+1038x^118+408x^119+52x^120+30x^121+12x^122+42x^123+12x^124+28x^126+12x^129+2x^174

The gray image is a linear code over GF(3) with n=531, k=7 and d=342.
This code was found by Heurico 1.16 in 0.0839 seconds.