The generator matrix

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

generates a code of length 59 over Z3[X]/(X^2) who´s minimum homogenous weight is 115.

Homogenous weight enumerator: w(x)=1x^0+12x^115+48x^117+144x^118+24x^120+2x^123+6x^124+2x^126+2x^132+2x^150

The gray image is a linear code over GF(3) with n=177, k=5 and d=115.
This code was found by Heurico 1.16 in 0.0217 seconds.