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

generates a code of length 72 over Z3[X]/(X^3) who´s minimum homogenous weight is 145.

Homogenous weight enumerator: w(x)=1x^0+66x^145+2x^147+6x^148+2x^150+4x^153

The gray image is a linear code over GF(3) with n=648, k=4 and d=435.
This code was found by Heurico 1.16 in 0.13 seconds.