The generator matrix

 1  0  1  1  1  1  1 2X^2+X  1  1  1 2X^2  1  1  1 2X^2+X  1 2X^2+2X  1  1  1  1  1  1  1 2X^2+X  1  1  1  0 2X  1  1  1  1  X  1  1  1
 0  1  1  2 2X^2+2X+1 2X^2 2X^2+2  1 2X+1 2X^2+X 2X^2+X+2  1 2X^2+1 2X^2+X 2X^2+X+2  1  X  1 2X^2+X+1 2X^2+2X+2 2X  1 X+2 X+1  2  1 2X^2+2 2X^2+2X+1 2X^2+X+2  1  1  2 X^2+2X+1 X^2+X+1 X^2+1 X^2+2X 2X  2  0
 0  0 2X  0  0 2X^2+X 2X^2+X 2X^2  X 2X^2+2X X^2+2X 2X^2+X X^2 X^2 X^2 2X X^2+X X^2+X  X X^2+X X^2+2X  X 2X^2+X 2X 2X^2+2X 2X^2  X 2X^2+2X 2X^2 X^2+2X 2X 2X 2X^2+2X X^2+2X X^2 2X^2+2X 2X 2X  0
 0  0  0 X^2  0 2X^2  0 2X^2  0 2X^2  0 X^2 2X^2 X^2 2X^2 2X^2 2X^2  0  0 X^2 2X^2 2X^2  0 2X^2 2X^2  0 2X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 2X^2 X^2 2X^2 X^2
 0  0  0  0 2X^2  0  0  0  0  0  0 2X^2 X^2 X^2 2X^2 2X^2 X^2 2X^2 2X^2 2X^2 2X^2  0 2X^2 X^2 X^2 X^2 X^2 X^2 X^2 2X^2  0 X^2 2X^2 X^2  0  0  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+216x^70+180x^71+1944x^72+1782x^73+2250x^74+5244x^75+4968x^76+7236x^77+8340x^78+7236x^79+7218x^80+6400x^81+3240x^82+612x^83+1278x^84+54x^85+378x^87+50x^90+12x^93+2x^96+2x^99

The gray image is a linear code over GF(3) with n=351, k=10 and d=207.
This code was found by Heurico 1.16 in 6.48 seconds.