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

generates a code of length 74 over Z3[X]/(X^3) who´s minimum homogenous weight is 145.

Homogenous weight enumerator: w(x)=1x^0+216x^145+42x^147+282x^148+18x^150+90x^151+14x^153+54x^154+6x^157+4x^159+2x^168

The gray image is a linear code over GF(3) with n=666, k=6 and d=435.
This code was found by Heurico 1.16 in 0.196 seconds.