The generator matrix
1 0 1 1 1 1 1 0 1 0 1 1 1 1 1 0 X 1 1 1 0 1 1 1 1 1 1 2X 1 1 1 0 2X 1 1 1 2X X 0 2X 1 1 2X 0 0 1 1 2X 1 1 1 1 1 1 X 1 1 1 1 X
0 1 1 2 0 1 2 1 2X+1 1 0 2 X+2 2X+1 0 1 1 0 2 2X+1 1 2 2X+1 0 2 2X+1 0 1 X+2 2 1 1 1 X 2X+1 X 1 1 1 1 2X+2 X 1 1 1 1 X+2 1 X+1 2X 2 X+2 2X+2 2X 1 1 X+1 1 X+1 1
0 0 2X 0 0 0 0 0 0 0 2X X X 2X 2X 2X 2X 2X 2X 0 X X 0 X 2X 2X 2X 2X 2X 0 0 X 2X X X X 2X X 2X 2X 0 2X 0 X X 2X X 2X X 2X 0 2X X 0 2X 0 0 X 2X 2X
0 0 0 X 0 0 0 X 2X X 0 2X X 2X 2X 0 2X 2X 0 X 2X X 2X 2X X X 2X 0 0 X X X 0 X 0 0 2X X 0 X X 0 0 0 0 2X 0 0 X 2X 2X 2X 0 2X X 2X 0 X 0 2X
0 0 0 0 X 0 X X X X X 2X 0 X X 0 2X 0 0 0 0 2X 2X 2X 2X X X 2X X 2X 2X X 0 0 2X X 0 0 X 0 0 X 2X 2X 0 2X 0 X X 0 2X 2X 2X 0 0 X X 0 2X 0
0 0 0 0 0 2X 2X 0 2X X 0 2X X X 2X 2X X X 2X 2X 0 0 X X 2X 0 0 2X 2X 0 2X 0 X 2X 2X 2X 2X 2X 2X 2X X X 0 2X 0 0 0 X 0 2X 2X X 0 0 X 0 2X 2X 0 0
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+108x^108+90x^109+90x^110+334x^111+192x^112+204x^113+464x^114+174x^115+168x^116+650x^117+180x^118+258x^119+584x^120+300x^121+318x^122+706x^123+228x^124+264x^125+464x^126+162x^127+138x^128+180x^129+102x^130+18x^131+50x^132+30x^133+30x^135+32x^138+18x^141+14x^144+4x^147+4x^150+2x^153
The gray image is a linear code over GF(3) with n=180, k=8 and d=108.
This code was found by Heurico 1.16 in 0.676 seconds.