The generator matrix
1 0 1 1 1 1 1 0 1 0 1 1 1 1 1 0 X 1 1 1 1 0 1 1 2X 1 1 1 X 1 2X 1 1 1 2X 1 1 1 X 1 2X 1 1 1 1 1 1 1 1 X 2X 1 1 1 2X 1 1 1 1 1 1 1 1 0
0 1 1 2 0 1 2 1 2X+1 1 0 2 X+2 2X+1 0 1 1 0 2 2X+1 0 1 2X+1 2 1 X 2X+1 X 1 2X+2 1 2X 2X+1 X+2 1 X+2 1 X+1 1 0 1 X+2 1 X+2 X+2 X X X+2 2 1 1 X+1 2X+2 1 1 2 2X 2 2 1 2X+2 2 X 1
0 0 2X 0 0 0 0 0 0 0 2X X X 2X 2X 2X 2X 2X 2X X 2X X X X X 2X X 0 0 2X X 2X X X 0 0 X 2X 0 X X X X X 0 0 0 0 2X 0 2X 2X X 2X 2X X 2X X 0 0 0 2X 0 2X
0 0 0 X 0 0 0 X 2X X 0 2X X 2X 2X 0 2X 2X 0 0 2X 2X 0 X 2X 0 2X 2X X 0 2X 2X X 2X 2X 2X 2X X X 2X X 2X 2X 2X 0 2X 0 X 2X 0 2X 2X 0 X X 0 X 0 X 2X 0 2X 0 0
0 0 0 0 X 0 X X X X X 2X 0 X X 0 2X 0 0 0 X 0 2X 2X 0 2X 2X 2X 2X X X 2X X 0 2X X 2X 0 0 0 2X X 0 X X 2X X 2X X X 2X 2X 2X 2X 2X 0 X X 0 X 0 0 X X
0 0 0 0 0 2X 2X 0 2X X 0 2X X X 2X 2X X X 2X 0 0 0 2X 0 X 2X X 0 2X 2X 0 X 0 X 0 2X 2X X 2X 2X 2X 0 2X X 0 2X X 2X 0 2X 2X 0 2X 0 2X 2X 2X 0 2X X X 0 2X 2X
generates a code of length 64 over Z3[X]/(X^2) who´s minimum homogenous weight is 115.
Homogenous weight enumerator: w(x)=1x^0+36x^115+222x^117+294x^118+204x^120+492x^121+308x^123+714x^124+394x^126+684x^127+306x^129+858x^130+258x^132+738x^133+258x^135+420x^136+126x^138+108x^139+14x^141+24x^142+50x^144+6x^145+8x^147+12x^150+16x^153+2x^156+2x^159+4x^162+2x^165
The gray image is a linear code over GF(3) with n=192, k=8 and d=115.
This code was found by Heurico 1.16 in 73 seconds.