The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 X 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 2X 1 2X 2X X X
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 2X+1 2 1 1 X+2 0 2 2X+1 1 0 2 2X+1 2X+1 X X 2X+1 0 2X+1 2X 1 1 2X 1 1 2X 0
0 0 2X 0 0 0 0 0 0 0 0 0 0 2X 2X X 2X X X 2X 0 2X 2X 2X 2X 2X 2X 2X 0 X 2X X X X 0 2X 0 2X X
0 0 0 X 0 0 0 0 0 0 0 2X 0 0 0 2X 2X X 2X X X 2X 2X 0 X 2X 0 2X 2X 0 X 2X X 2X 2X 0 X X 0
0 0 0 0 X 0 0 0 X 2X 2X X 2X X 2X 0 2X X X X 2X 0 0 0 2X X X X 2X 0 0 X 0 2X X X 2X X 2X
0 0 0 0 0 2X 0 X 2X 2X 2X 0 X 0 2X X X X X 2X 0 0 X X 0 X 0 2X 2X 2X X 0 X 0 2X X 2X 2X 2X
0 0 0 0 0 0 X 2X 2X 2X 0 2X 2X X X 0 2X 0 0 X 0 2X X 0 0 2X 2X 2X 0 X X X X 0 2X X X 2X 0
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+106x^63+18x^64+42x^65+304x^66+162x^67+126x^68+602x^69+282x^70+330x^71+1164x^72+672x^73+816x^74+1940x^75+738x^76+1008x^77+2436x^78+1038x^79+1014x^80+2258x^81+906x^82+708x^83+1332x^84+396x^85+270x^86+450x^87+138x^88+60x^89+206x^90+24x^91+92x^93+22x^96+18x^99+4x^102
The gray image is a linear code over GF(3) with n=117, k=9 and d=63.
This code was found by Heurico 1.16 in 3.43 seconds.