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

generates a code of length 79 over Z3[X]/(X^3) who´s minimum homogenous weight is 150.

Homogenous weight enumerator: w(x)=1x^0+174x^150+448x^153+2268x^156+3114x^159+158x^162+96x^165+114x^168+120x^171+66x^174+2x^234

The gray image is a linear code over GF(3) with n=711, k=8 and d=450.
This code was found by Heurico 1.16 in 0.569 seconds.