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

generates a code of length 75 over Z3[X]/(X^3) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+70x^144+24x^147+1986x^150+60x^153+30x^156+12x^159+2x^162+2x^225

The gray image is a linear code over GF(3) with n=675, k=7 and d=432.
This code was found by Heurico 1.16 in 0.203 seconds.