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 X 1 1 0 1 1 X X 1 1 0 2X 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 2X 1 1 X 1 1 1 1
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 2 X+2 1 1 X 1 1 X 2X+2 1 1 2X+2 2X 2 X+1 2X+2 1 2X 2X+2 1 2X+1 X X+1 2X X 1 1 X+1 2X+1 1 2X+1 2X+2 2X+2 0
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 0 2X X 0 X 2X 2X X 0 2X X X 0 0 2X 0 2X 2X 0 2X X 0 0 2X X X 2X 0 X X 0 X 0 0
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 X 0 X X X 0 0 0 X 2X 0 0 2X X X 0 X 0 2X X 2X 2X 2X X 2X X 2X 0 2X 2X X 0 X 0
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 X 2X X X 2X 0 0 2X X 0 0 2X 2X 2X 2X 0 0 0 2X 2X 2X 0 0 X X X 0 X 2X 2X 0 0 X 2X 2X
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 0 2X 0 2X 2X X 2X 2X X 2X 2X 0 0 2X 2X 0 X 0 X 0 0 X 0 X 0 0 X X X 2X X X X X
generates a code of length 62 over Z3[X]/(X^2) who´s minimum homogenous weight is 111.
Homogenous weight enumerator: w(x)=1x^0+44x^111+48x^112+150x^113+100x^114+258x^115+282x^116+120x^117+372x^118+396x^119+102x^120+438x^121+492x^122+70x^123+594x^124+564x^125+66x^126+546x^127+498x^128+58x^129+432x^130+378x^131+48x^132+174x^133+126x^134+20x^135+54x^136+24x^137+30x^138+6x^140+22x^141+12x^144+14x^147+10x^150+6x^153+4x^156+2x^159
The gray image is a linear code over GF(3) with n=186, k=8 and d=111.
This code was found by Heurico 1.16 in 0.703 seconds.