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

generates a code of length 77 over Z3[X]/(X^3) who´s minimum homogenous weight is 153.

Homogenous weight enumerator: w(x)=1x^0+174x^153+486x^154+54x^156+8x^162+6x^180

The gray image is a linear code over GF(3) with n=693, k=6 and d=459.
This code was found by Heurico 1.16 in 0.303 seconds.