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  0  0  0  0  X 2X 2X  0  0  X  X  X  X  X  X  X  0 2X  0 2X  0 2X  0  X 2X  X 2X 2X  0  0 2X  X  0  X 2X 2X  0 2X  X  X  0  0  0  X  X  X  0  X  0  X  0  X  0  0  X  X 2X 2X 2X 2X 2X 2X 2X 2X  0 2X 2X 2X  X 2X  0  0  0
 0  0  X  0  0  X 2X  0 2X  0  X  X 2X 2X  0  X  0  X  X  X  X  0  0 2X 2X  X  X 2X  0 2X  0  X  X  0 2X 2X 2X  0 2X  X  X  0 2X 2X 2X  X 2X  0 2X  X  0 2X  0  X  X  X 2X  0  0 2X 2X  0  X  X  0 2X 2X  X  0  X  0 2X  0  0  0
 0  0  0  X  0 2X 2X  X  0  X  X  0  0  X 2X  X  X 2X 2X  0  0 2X 2X 2X 2X 2X  X  X  0  X 2X  X 2X 2X  X 2X  X  0  0  0  X  0  0 2X  0  0  0  X  X 2X 2X  0  0  X 2X  0 2X  X  0 2X  X  X  0 2X  X  0 2X  X 2X 2X  0 2X  X  0  0
 0  0  0  0  X 2X 2X 2X 2X 2X  0 2X  0  0 2X 2X  0  X  0  0 2X 2X  X 2X  X 2X  0 2X  0  0 2X 2X  X  0  0  0 2X 2X  0  X  X  X  X  0 2X  0  X 2X 2X  0  0 2X 2X  0  X  X  X  X  X  X  X  X 2X 2X  0  0 2X 2X  0  0 2X  0  X  X  X

generates a code of length 75 over Z3[X]/(X^2) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+70x^144+24x^147+528x^150+60x^153+30x^156+12x^159+2x^162+2x^225

The gray image is a linear code over GF(3) with n=225, k=6 and d=144.
This code was found by Heurico 1.16 in 0.0944 seconds.