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

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+18x^144+30x^146+64x^147+72x^148+72x^149+1708x^150+72x^151+36x^152+42x^153+18x^154+24x^155+26x^156+2x^159+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 0.237 seconds.