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

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+172x^72+108x^75+1566x^78+306x^81+24x^90+8x^99+2x^108

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 0.176 seconds.