The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 X 1 1 1 1 1 0 1 1 1 0 1 1 1 2X 1 1 0 2X 1 1 1 1 X 1 1 1 1 2X 2X 1 1 0 1 1 1 X 1 X 1 1 X 2X 2X 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 2 2X+1 1 1 X+2 X 2X+1 2 0 1 2X+1 2 2X+1 1 0 X+2 0 1 2X 2X+1 1 1 2 2X+1 2X+1 X+2 1 2X+2 X+1 X+2 2X+1 1 1 X X+1 1 1 2X+1 0 2X X 1 X+2 0 2X 1 1 2X+1 0
0 0 2X 0 0 0 0 0 0 2X X 2X 2X 2X 2X 0 2X 0 2X X 2X 0 X 0 0 0 0 2X 2X 0 X 0 X 2X X X X 2X X 2X 2X 2X X 2X 0 2X 2X X 2X 0 0 0 X 0 0 2X 2X 2X 0 2X X 0
0 0 0 X 0 0 0 0 0 0 0 0 0 0 2X X 2X X 0 2X 0 2X 2X X 2X 0 X X 0 X 0 2X 2X X 2X X 0 2X 2X 0 X 2X X 0 0 X 2X 2X X X 2X 0 0 2X X 0 2X 0 2X 0 2X 0
0 0 0 0 X 0 0 0 0 0 0 0 0 0 2X 2X X 0 X 2X X 0 2X 2X 0 2X X 2X X X X 0 0 0 X 2X X 2X 0 2X X X 0 2X 2X 2X X 0 0 2X 2X 0 X X 0 X 2X 2X 2X 0 0 0
0 0 0 0 0 2X 0 0 X 2X 2X X 2X 0 2X 2X 2X X 0 X X X 0 0 0 2X 2X 2X X 0 2X 2X X X X 0 0 X 0 0 2X 2X 2X 2X 2X X 2X X X X 2X 0 2X 0 0 2X 0 X 2X 0 0 X
0 0 0 0 0 0 X 0 X 0 X X X 2X 2X 0 X 2X 2X 0 0 0 2X X 0 2X X X 2X 0 0 X X 0 X 0 0 2X 2X X 0 X 2X X 0 2X X X X X X 2X 2X X 2X 2X X 2X X 2X 2X 0
0 0 0 0 0 0 0 X X X X 0 2X X 2X X X X 0 0 0 2X X X 2X X 0 0 X 0 2X 2X 0 X 2X 0 X 0 X X X 2X 2X 2X 2X 2X 0 X 0 X X 0 0 0 2X 2X 2X X 0 2X X 0
generates a code of length 62 over Z3[X]/(X^2) who´s minimum homogenous weight is 102.
Homogenous weight enumerator: w(x)=1x^0+92x^102+6x^104+228x^105+60x^106+114x^107+384x^108+216x^109+474x^110+450x^111+756x^112+954x^113+500x^114+1656x^115+2130x^116+546x^117+2898x^118+3366x^119+614x^120+4374x^121+4740x^122+554x^123+5634x^124+5412x^125+616x^126+4896x^127+4446x^128+584x^129+3348x^130+2826x^131+612x^132+1722x^133+1248x^134+430x^135+576x^136+462x^137+386x^138+108x^139+60x^140+276x^141+6x^143+146x^144+84x^147+42x^150+10x^153+4x^156+2x^159
The gray image is a linear code over GF(3) with n=186, k=10 and d=102.
This code was found by Heurico 1.16 in 52.8 seconds.