The generator matrix

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

generates a code of length 60 over Z3[X]/(X^2) who´s minimum homogenous weight is 111.

Homogenous weight enumerator: w(x)=1x^0+660x^111+1134x^114+1190x^117+1074x^120+954x^123+688x^126+474x^129+246x^132+108x^135+24x^138+6x^141+2x^144

The gray image is a linear code over GF(3) with n=180, k=8 and d=111.
This code was found by Heurico 1.16 in 6.91 seconds.