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

generates a code of length 72 over Z3[X]/(X^3) who´s minimum homogenous weight is 138.

Homogenous weight enumerator: w(x)=1x^0+32x^138+54x^141+2028x^144+38x^147+18x^150+12x^153+2x^156+2x^216

The gray image is a linear code over GF(3) with n=648, k=7 and d=414.
This code was found by Heurico 1.16 in 0.179 seconds.