The generator matrix

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

generates a code of length 60 over Z3[X]/(X^2) who´s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+680x^108+1818x^111+2782x^114+3028x^117+3314x^120+2958x^123+2614x^126+1586x^129+684x^132+184x^135+32x^138+2x^141

The gray image is a linear code over GF(3) with n=180, k=9 and d=108.
This code was found by Heurico 1.16 in 5.6 seconds.