The generator matrix
1 0 0 1 1 1 1 1 0 2X 1 1 1 X 1 1 1 1 1 0 1 0 1 1 1 0 2X X 0 1 1 1 1 1 2X 1 1 1 1 1 X 1 X 2X 2X 0 1 1 1 1 1 1 0 X 1 1 1 1 1 1
0 1 0 1 0 2 1 2 1 1 0 2X+1 2X+2 1 0 2X+1 2X+1 2X 0 2X 2X+2 1 2 2X+1 X+2 1 1 1 X 0 2X+1 2 2X 1 1 X+2 2X+1 0 2X 2 X 2 2X 1 1 1 X+2 0 0 X+1 X 2X 1 2X 1 2 2X+2 1 2 0
0 0 1 2 1 2 1 0 2 2X+1 2 2X 2X+1 1 0 2X+2 1 2X+1 2 1 2X+1 X X 2X 2 2 X+1 X 1 X+1 2X 2X+2 0 X+2 X 1 1 1 2X+2 2X+1 1 0 1 X+2 1 2X+1 2X+2 2 1 0 2X 0 X 1 2X+1 2X 2 2X+1 0 0
0 0 0 2X 0 0 0 0 0 0 0 0 2X 0 0 X X X X 2X 2X 2X 2X X 2X 2X 2X X X 0 2X X 0 0 X 0 X 2X 2X X X 2X X X 2X 2X 2X 2X 2X 0 0 2X 2X 0 0 2X X 2X 0 0
0 0 0 0 2X 0 0 0 0 0 X 2X 0 0 X X 0 X 2X 0 X 0 2X 0 X X 2X X 2X X 2X 2X 2X 2X X X X 2X X 2X 2X 2X 0 0 X X 0 2X 0 0 2X X X 2X 2X X 0 2X X 0
0 0 0 0 0 X 0 X X 2X X 2X 2X 0 2X X 0 0 X 2X 0 0 X 2X X 0 0 X 2X X X 0 0 0 X 0 2X 0 2X 2X X 0 0 X 2X 2X X 2X X 2X X 2X 2X X 2X X 2X 2X 0 0
0 0 0 0 0 0 X X X X 0 0 2X 2X X 0 2X 0 0 0 0 2X 2X 2X 2X 2X 0 2X X X X X 2X 0 X X X X 0 0 X X 2X 2X 0 X X 2X X X 0 X 2X 0 X 0 2X X 0 X
generates a code of length 60 over Z3[X]/(X^2) who´s minimum homogenous weight is 102.
Homogenous weight enumerator: w(x)=1x^0+100x^102+18x^103+192x^104+350x^105+234x^106+666x^107+890x^108+636x^109+1518x^110+1394x^111+1068x^112+2502x^113+2366x^114+1698x^115+3570x^116+2930x^117+2256x^118+5088x^119+3244x^120+2490x^121+5040x^122+3434x^123+2364x^124+4074x^125+2400x^126+1446x^127+2424x^128+1480x^129+636x^130+852x^131+704x^132+240x^133+276x^134+210x^135+36x^136+42x^137+84x^138+50x^141+22x^144+16x^147+8x^150
The gray image is a linear code over GF(3) with n=180, k=10 and d=102.
This code was found by Heurico 1.16 in 43.8 seconds.