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 X 1 1 1 1 1 1 0 1 1 1 1 1 1 1 X 1 1 X 1 1 0 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 1 X 2 2X+1 2X X X 1 2X+2 1 2X 2X+1 X+1 X+2 X+2 1 2X+1 X 1 X+2 X+1 1 2X+1
0 0 2X 0 0 0 0 0 0 0 2X X X 2X 2X 2X 2X 2X 2X 0 X X 0 0 X 2X 0 X 2X 0 2X 2X 0 X X X X X 0 0 X 2X X 0 0 X
0 0 0 X 0 0 0 X 2X X 0 2X X 2X 2X 0 2X 2X 0 X 2X X 2X X 0 2X X X 2X X X 0 0 0 2X 2X 2X 2X 0 X 0 0 X 0 0 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 2X 2X 2X 2X 2X X X 2X 0 2X 2X 0 0 2X 0 0 X X X X 2X
0 0 0 0 0 2X 2X 0 2X X 0 2X X X 2X 2X X X 2X 2X 0 0 X 0 0 2X 2X X X X 0 2X X X X 2X X 2X 2X X 2X 2X X 2X X X
generates a code of length 46 over Z3[X]/(X^2) who´s minimum homogenous weight is 81.
Homogenous weight enumerator: w(x)=1x^0+214x^81+162x^82+164x^84+408x^85+222x^87+822x^88+454x^90+822x^91+350x^93+1122x^94+394x^96+690x^97+232x^99+312x^100+58x^102+36x^103+28x^105+38x^108+20x^111+4x^114+6x^117+2x^120
The gray image is a linear code over GF(3) with n=138, k=8 and d=81.
This code was found by Heurico 1.16 in 28 seconds.