The generator matrix

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

generates a code of length 39 over Z3[X]/(X^3) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+396x^72+108x^74+612x^75+810x^76+432x^77+1422x^78+1620x^79+432x^80+264x^81+252x^84+198x^87+12x^90+2x^108

The gray image is a linear code over GF(3) with n=351, k=8 and d=216.
This code was found by Heurico 1.16 in 0.205 seconds.