The generator matrix

 1  0  0  0  1  1  1 2X^2  1  1  1  1  1  1 X^2 X^2+2X 2X^2+2X  1 2X^2+X  1  1 X^2+2X  1  1  1  1 2X^2+2X  1  1  1 X^2+X X^2  1  1 2X^2  1  1 2X  1
 0  1  0  0 2X^2  1 X^2+1  1  X X^2 X+1 2X^2+2 X^2+2X+2 2X^2+2X+2  1  1 2X^2+2X 2X^2+X+1 2X^2 2X^2+2 2X^2+1  1 X^2+2X X^2+2X+1 2X^2+X 2X+1  1 X^2+X 2X^2+X+2 2X^2+X+2  1  1  1 X^2+X+1  1 2X^2+X 2X X^2+X X^2
 0  0  1  0 2X^2+2X+1 2X+1 2X^2+X+2 2X^2+2X+1 X+1 2X X^2+2X X^2+2X+2 X^2 2X^2+1 2X+2 X^2+2X+1  1 X^2+X+2  1 X^2 X^2+1 2X^2+X+1 X+2  X X^2+2 2X^2+2X+1 X^2+2X+2 2X+1 2X^2+X+2  2 2X^2+X 2X^2+X  2 2X^2+X+2 2X^2+2  2 2X^2+2X  1 2X^2+X
 0  0  0  1 2X^2+2X+2 X^2 X^2+2X+2 X^2+2X+2  1 X+2 X^2+X+1 X^2+X+2 X^2+1 X^2+X 2X^2+2X+1 X^2+X 2X^2+X+1 2X^2+2X 2X+2 X^2+X 2X^2+X+1  1 X^2+X+1 X^2+2X 2X^2+X X^2+2 2X^2+X+2 2X 2X+1 2X^2 X^2+2X+1 X^2+X+2 2X^2+X+2  0 2X^2+2X X^2+2 X^2+X+1 X^2+X 2X

generates a code of length 39 over Z3[X]/(X^3) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+360x^68+1076x^69+3738x^70+5988x^71+11870x^72+16758x^73+25668x^74+37744x^75+50808x^76+59892x^77+70274x^78+78456x^79+63936x^80+49734x^81+29178x^82+15258x^83+7286x^84+2706x^85+372x^86+104x^87+120x^88+78x^89+30x^90+6x^92

The gray image is a linear code over GF(3) with n=351, k=12 and d=204.
This code was found by Heurico 1.16 in 284 seconds.