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 1 0 1 1 1 0 0 1 1 1 2X 1 2X 1 2X 1 1 2X 0 1 2X 1 1 1 X 1 1 1 2X 1 X X 1 1 X 2X X X 0 1 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 2 2X+1 1 1 X+2 0 2X+1 0 2X+1 2 1 0 2 2X+1 1 1 X 2X+1 X+1 1 X+2 1 2X+1 1 X X 1 1 2X 1 2 2X+1 2X 1 2X+2 2X+2 2X 1 2X+2 1 1 2X+2 X+2 1 1 1 1 1 2X+1 0 0
0 0 2X 0 0 0 0 0 0 2X X 2X 2X 2X 2X 0 2X 0 2X 2X 0 2X 2X 0 2X 0 X 0 2X 0 X 0 X X 2X X 2X X 0 X 2X X 0 X 0 X 0 0 2X 2X 2X X 0 2X X X X 2X 2X 2X X X X 0
0 0 0 X 0 0 0 0 0 0 0 0 0 0 2X X 2X X 0 X X 2X 2X X 0 X X 0 X X X X X 0 0 X X X 2X X 2X 0 X 2X 2X 0 X X X 0 0 0 0 2X X 0 X 0 0 X X 2X 2X 0
0 0 0 0 X 0 0 0 0 0 0 0 0 0 2X 2X X 0 2X X 2X 0 2X X 2X 0 2X 2X 0 2X 0 0 X 2X X X 2X 0 2X 0 2X 2X 0 2X X 2X X 0 X 2X X 0 X X 0 X X 0 X 2X 0 2X X 0
0 0 0 0 0 2X 0 0 X 2X 2X X 2X 0 2X 2X 2X X 0 0 0 X X X 0 0 0 X 2X 2X 0 X X X 2X 2X X X 0 0 0 0 0 2X 0 X X X X X 0 X 2X 0 2X 0 2X 0 2X 2X 0 X 0 0
0 0 0 0 0 0 X 0 X 0 X X X 2X 2X 0 X 2X 2X 0 2X X 2X 0 0 2X X 2X 0 X 2X X X 0 0 X 2X X 0 X X 2X 0 0 X X X X 2X 0 2X 0 0 0 0 0 2X 2X 2X X X 2X 0 0
0 0 0 0 0 0 0 X X X X 0 2X X 2X X X X X 2X 2X 2X X 0 X X 2X X X 0 2X X 2X X 0 0 0 0 X 0 2X X X X 0 2X 2X 0 X 2X 0 X 2X 0 2X 2X X 0 2X 0 2X 0 2X X
generates a code of length 64 over Z3[X]/(X^2) who´s minimum homogenous weight is 105.
Homogenous weight enumerator: w(x)=1x^0+62x^105+202x^108+90x^109+24x^110+332x^111+228x^112+120x^113+422x^114+582x^115+504x^116+502x^117+1254x^118+1470x^119+506x^120+2550x^121+2928x^122+524x^123+3984x^124+4692x^125+630x^126+4854x^127+6006x^128+592x^129+5202x^130+5340x^131+628x^132+3912x^133+3522x^134+572x^135+2280x^136+1248x^137+486x^138+924x^139+360x^140+422x^141+270x^142+30x^143+276x^144+108x^145+212x^147+6x^148+92x^150+58x^153+30x^156+10x^159+2x^165
The gray image is a linear code over GF(3) with n=192, k=10 and d=105.
This code was found by Heurico 1.16 in 54.8 seconds.