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 0 1 1 2X 1 1 1 0 1 1 1 2X 1 1 X 2X 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 X+1 X+2 1 1 0 2X+1 2 2X+1 0 1 2 X 1 2X+1 X+2 1 2 1 0 1 2X+1 2X 2 1 X 2X+1 1 1 0 2X+2 X 2X 1 X+1 X+2 2X+1 2X+2 1 1 2X+2 1 X+1 2X+1 0 2 X+2 2X+1 1
0 0 2X 0 0 0 0 0 0 0 0 0 0 X 0 X 2X X 2X X 2X 0 X X 2X X 2X 0 2X 2X 2X X 2X X 0 0 2X X 2X 2X 0 2X 2X 0 2X 0 2X X 0 2X X 2X 2X 0 0 X X 0 0 X X
0 0 0 X 0 0 0 0 0 0 0 2X 0 0 2X X 2X 0 X 2X 0 X X 2X 0 X X X 2X 0 X X X X 2X X 2X 0 2X X 2X 0 X 2X 0 2X 0 2X 2X X 0 0 2X 2X 0 X 2X X 0 2X 0
0 0 0 0 X 0 0 0 X 2X 2X 0 X 2X 2X 0 0 2X X X 2X 0 X 2X 0 2X X X X 2X 0 0 X 0 2X 0 X 0 0 2X 0 2X 0 0 2X 2X 2X 0 2X 2X X X X 2X 2X X X 2X 2X 2X X
0 0 0 0 0 2X 0 X 2X 2X 2X 2X 0 X 2X 2X 2X 0 2X 2X X 2X 0 X 2X X 0 2X 0 0 X 0 X 2X 0 X 0 0 0 0 2X 0 0 0 2X 2X 2X 0 0 X X X X X 2X X X X 2X X 0
0 0 0 0 0 0 X 2X 2X 2X 0 2X 2X 2X X 2X 0 2X 0 2X 2X 2X 2X 2X 2X 0 0 0 2X 0 2X X X X 2X 2X X 0 2X 2X 0 2X X 0 0 0 X 0 X X X 2X 2X 2X X X X X X X X
generates a code of length 61 over Z3[X]/(X^2) who´s minimum homogenous weight is 105.
Homogenous weight enumerator: w(x)=1x^0+84x^105+36x^106+230x^108+282x^109+408x^111+606x^112+630x^114+1344x^115+762x^117+2046x^118+990x^120+2502x^121+1068x^123+2586x^124+990x^126+2028x^127+610x^129+1296x^130+356x^132+300x^133+156x^135+72x^136+130x^138+24x^139+68x^141+48x^144+22x^147+8x^150
The gray image is a linear code over GF(3) with n=183, k=9 and d=105.
This code was found by Heurico 1.16 in 6.4 seconds.