The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 X 1 1 X 1 X 1 1 X X X 1 1
0 X 0 0 0 0 0 0 0 0 0 0 0 X X 2X 2X 2X X 2X X X X X X 2X X X 0 X 0 X 2X X 0 0 X X X
0 0 X 0 0 0 0 0 0 0 0 X X 2X X 0 X 2X 2X 2X 0 0 X 2X X X 0 2X X 0 X 0 2X 0 X X 2X 0 2X
0 0 0 X 0 0 0 0 X 2X 2X 2X 2X 2X X 0 X 2X 0 0 0 2X 2X X 2X 0 X X 2X X X X 0 X X 0 X X 0
0 0 0 0 X 0 0 X 2X 0 2X 2X X X X 2X X X 0 2X X 2X 2X X X X 2X X X 2X 0 0 X 0 X X 0 X 2X
0 0 0 0 0 X 0 2X 2X X 0 2X 2X X 2X 2X X 2X 2X X 2X X 2X X X 0 X 0 2X 2X 2X 0 2X X X 2X 2X 0 2X
0 0 0 0 0 0 X 2X 2X 2X 2X X 0 X X 0 0 X 2X X X X X 0 2X 2X 0 X X 0 0 0 2X X 2X 0 2X 0 2X
generates a code of length 39 over Z3[X]/(X^2) who´s minimum homogenous weight is 63.
Homogenous weight enumerator: w(x)=1x^0+84x^63+200x^66+24x^67+240x^69+180x^70+248x^72+576x^73+210x^75+1086x^76+228x^78+1332x^79+266x^81+936x^82+222x^84+240x^85+192x^87+168x^90+70x^93+42x^96+16x^99
The gray image is a linear code over GF(3) with n=117, k=8 and d=63.
This code was found by Heurico 1.16 in 0.675 seconds.