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  X  X  1  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X
 0 X^2  0  0 X^2  0 X^2 X^2 2X^2  0  0 X^2 X^2  0 2X^2 X^2 2X^2 2X^2  0 X^2 2X^2  0 X^2 2X^2 2X^2 2X^2 2X^2  0  0  0 X^2 X^2  0 X^2 X^2 2X^2  0  0 X^2 X^2  0 2X^2 X^2 2X^2 2X^2  0 X^2 2X^2 X^2 X^2  0 X^2 2X^2 X^2  0  0  0 2X^2 X^2 X^2 2X^2 2X^2 X^2 2X^2  0 2X^2 X^2 2X^2 2X^2  0  0  0 X^2 2X^2
 0  0 X^2  0 2X^2 X^2 2X^2 X^2 2X^2  0 X^2 X^2  0 2X^2  0  0 X^2 X^2 2X^2 2X^2 2X^2 2X^2 X^2  0  0 X^2 2X^2  0  0 X^2 2X^2 X^2 X^2 2X^2  0 2X^2  0 X^2 X^2  0 2X^2  0  0 X^2 X^2 2X^2 2X^2 2X^2 X^2  0 2X^2 2X^2  0 X^2  0 X^2 2X^2 X^2 X^2  0  0 X^2 2X^2 2X^2 X^2 2X^2  0 X^2 2X^2 2X^2  0 2X^2 2X^2  0
 0  0  0 X^2 2X^2 2X^2  0 2X^2 2X^2 2X^2 X^2  0 2X^2  0 2X^2 X^2 X^2  0 X^2 X^2 X^2 2X^2 X^2  0 X^2 2X^2  0  0 X^2 2X^2 2X^2 2X^2 X^2 X^2 X^2 2X^2 2X^2  0  0  0 X^2 X^2 2X^2 2X^2 X^2  0  0  0 X^2  0 2X^2  0 2X^2 2X^2 2X^2 2X^2  0 2X^2  0 2X^2  0  0 2X^2 2X^2  0 X^2 X^2 X^2  0 2X^2 X^2 X^2 X^2 X^2

generates a code of length 74 over Z3[X]/(X^3) who´s minimum homogenous weight is 146.

Homogenous weight enumerator: w(x)=1x^0+102x^146+32x^147+486x^148+54x^149+32x^150+8x^153+4x^156+4x^159+6x^173

The gray image is a linear code over GF(3) with n=666, k=6 and d=438.
This code was found by Heurico 1.16 in 72.8 seconds.