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

generates a code of length 74 over Z3[X]/(X^3) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+18x^144+48x^145+144x^146+32x^147+1692x^148+144x^149+16x^150+36x^151+36x^152+8x^153+6x^154+4x^156+2x^222

The gray image is a linear code over GF(3) with n=666, k=7 and d=432.
This code was found by Heurico 1.16 in 0.227 seconds.