The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 X 1 1 1 1 0 1 1 1 1 0 1 X 1 1 1 0 1 X 1 1 1 1 1 0 1 1 1 1 1 2X 1 1 1 1 1 1 1 1 1 X 1 X 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 X+1 2 1 1 2X+1 2 0 X+2 1 2 2X+1 0 X+1 1 2X+2 1 2X+1 2 X 1 X+2 1 2X+1 2X 2X 2X+2 X 1 X+1 X+2 2X 2X+1 0 1 X+1 0 X 2X+1 2X+1 2 2X X+2 X 1 0 0 0
0 0 2X 0 0 0 0 0 0 0 0 0 0 X X 2X 2X X 2X 2X X 2X 0 X X 2X X 0 0 0 X 2X X 0 2X 0 2X X 0 2X X 2X X X 0 X X X 2X X 0 2X X X X X 2X 0 X 0
0 0 0 X 0 0 0 0 0 0 0 2X 0 0 2X X 2X 0 2X 2X 2X X 2X 0 2X 0 X 2X X X 0 2X X 2X 0 2X X 0 0 X X X 0 X X X 2X 0 2X 2X X 2X 2X X X 2X X 2X X X
0 0 0 0 X 0 0 0 X 2X 2X 0 X 2X X 0 0 X 2X 2X 0 0 2X 0 X 2X 2X X 2X X 0 X X 2X 0 0 0 2X 2X 0 X 2X 0 2X 2X 0 X 0 X 2X X 2X 0 X X 0 X X 0 X
0 0 0 0 0 2X 0 X 2X 2X 2X 2X 0 X 2X 0 X 2X X 2X X X 0 0 X X X 0 X X 0 0 X X 2X 2X 0 2X 0 2X X X 2X 2X X 2X X 0 X 0 0 2X 0 2X X X 2X 2X 2X 0
0 0 0 0 0 0 X 2X 2X 2X 0 2X 2X 2X 0 X 2X X 0 0 0 X 2X X 2X X 0 2X 0 0 2X X X 0 2X X X 2X 2X 0 0 X X X 2X 2X 0 0 X X X X X X X X X X 0 0
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+48x^102+18x^103+6x^104+190x^105+102x^106+72x^107+478x^108+204x^109+186x^110+832x^111+342x^112+408x^113+1070x^114+564x^115+738x^116+1688x^117+678x^118+816x^119+2118x^120+906x^121+948x^122+2008x^123+762x^124+792x^125+1180x^126+462x^127+294x^128+712x^129+240x^130+96x^131+346x^132+84x^133+18x^134+112x^135+6x^136+60x^138+6x^139+54x^141+22x^144+10x^147+4x^150+2x^153
The gray image is a linear code over GF(3) with n=180, k=9 and d=102.
This code was found by Heurico 1.16 in 6.23 seconds.