The generator matrix

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

generates a code of length 39 over Z3[X]/(X^3) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+900x^71+1084x^72+1746x^73+4290x^74+4106x^75+5166x^76+7926x^77+7214x^78+7182x^79+8388x^80+4454x^81+2844x^82+2634x^83+808x^84+72x^85+120x^86+58x^87+36x^89+14x^90+6x^92

The gray image is a linear code over GF(3) with n=351, k=10 and d=213.
This code was found by Heurico 1.16 in 4.12 seconds.