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

generates a code of length 76 over Z3[X]/(X^3) who´s minimum homogenous weight is 150.

Homogenous weight enumerator: w(x)=1x^0+114x^150+486x^152+96x^153+18x^156+6x^159+2x^162+6x^177

The gray image is a linear code over GF(3) with n=684, k=6 and d=450.
This code was found by Heurico 1.16 in 0.283 seconds.