The generator matrix

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

generates a code of length 39 over Z3[X]/(X^3) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+406x^69+930x^70+2256x^71+4092x^72+5100x^73+9468x^74+12270x^75+15042x^76+23826x^77+23206x^78+22002x^79+24474x^80+16628x^81+8466x^82+5400x^83+2292x^84+810x^85+168x^86+130x^87+108x^88+18x^89+24x^90+24x^91+6x^94

The gray image is a linear code over GF(3) with n=351, k=11 and d=207.
This code was found by Heurico 1.16 in 35.7 seconds.