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  X  X 2X^2  X
 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 2X^2+X X^2+X 2X X^2+2X  X  X  X 2X^2+2X  X  X
 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  0 2X^2 2X^2  0 2X^2 X^2 2X^2  0  0 X^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+180x^150+108x^151+162x^152+168x^153+54x^154+48x^156+2x^162+6x^174

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 0.217 seconds.