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  1  X  1  X  1
 0  X 2X  0 2X^2+X 2X 2X^2+X X^2+2X  0 X^2  0 X^2 2X^2+X X^2+X X^2 2X 2X^2+2X 2X^2+X  X X^2  X 2X^2  X 2X 2X^2+2X 2X^2+2X 2X^2+2X  0  0 X^2 X^2 2X^2+X 2X^2+X X^2+X X^2+X 2X^2+X X^2+X 2X^2+X 2X^2
 0  0 X^2  0 X^2  0 2X^2 2X^2 X^2 2X^2 X^2 2X^2 2X^2  0 X^2  0 2X^2 X^2 X^2  0 2X^2 2X^2  0 X^2  0 X^2 2X^2  0 X^2 X^2  0 2X^2 X^2  0 2X^2  0 X^2 X^2  0
 0  0  0 X^2 2X^2 X^2 X^2 2X^2 2X^2 X^2  0 2X^2 2X^2 2X^2 X^2 2X^2 X^2  0 X^2 2X^2  0  0 X^2 2X^2  0 X^2  0 2X^2 X^2  0  0  0 X^2  0 X^2 2X^2 X^2  0  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+12x^72+192x^74+136x^75+360x^77+982x^78+360x^80+12x^81+24x^83+60x^84+36x^86+8x^87+2x^90+2x^111

The gray image is a linear code over GF(3) with n=351, k=7 and d=216.
This code was found by Heurico 1.16 in 0.034 seconds.