The generator matrix

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

generates a code of length 60 over Z3[X]/(X^2) who´s minimum homogenous weight is 105.

Homogenous weight enumerator: w(x)=1x^0+574x^105+2566x^108+4694x^111+6666x^114+9236x^117+10296x^120+10134x^123+7920x^126+4704x^129+1760x^132+376x^135+64x^138+36x^141+16x^144+6x^147

The gray image is a linear code over GF(3) with n=180, k=10 and d=105.
This code was found by Heurico 1.16 in 50.1 seconds.