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

generates a code of length 77 over Z3[X]/(X^3) who´s minimum homogenous weight is 150.

Homogenous weight enumerator: w(x)=1x^0+22x^150+36x^151+144x^152+24x^153+1710x^154+144x^155+18x^156+36x^157+36x^158+12x^159+2x^162+2x^231

The gray image is a linear code over GF(3) with n=693, k=7 and d=450.
This code was found by Heurico 1.16 in 0.261 seconds.