The generator matrix

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

generates a code of length 60 over Z3[X]/(X^2) who´s minimum homogenous weight is 115.

Homogenous weight enumerator: w(x)=1x^0+42x^115+66x^116+236x^117+36x^118+42x^119+34x^120+48x^121+16x^123+12x^124+42x^125+112x^126+18x^127+12x^128+2x^129+6x^130+2x^132+2x^153

The gray image is a linear code over GF(3) with n=180, k=6 and d=115.
This code was found by Heurico 1.16 in 50.8 seconds.