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^2  0  0  0  0  0  0  0  0 2X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 2X^2  0 X^2  0 X^2  0 2X^2 2X^2  0 X^2 X^2 X^2 X^2 2X^2  0 X^2 2X^2  0  0 2X^2 2X^2  0 2X^2 2X^2 2X^2 X^2 2X^2  0  0 X^2 2X^2 X^2 X^2  0 X^2 2X^2  0 2X^2 2X^2 2X^2  0 X^2 2X^2 2X^2  0 X^2 2X^2  0 X^2 2X^2 2X^2  0 X^2 2X^2  0 X^2
 0  0 X^2  0  0  0 X^2 X^2 X^2 2X^2  0 X^2 2X^2  0 2X^2 2X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0 2X^2 X^2 X^2 2X^2 2X^2  0 X^2 2X^2 2X^2 2X^2 2X^2  0  0 2X^2 2X^2 X^2 2X^2  0 2X^2 X^2 2X^2  0 X^2  0 X^2 2X^2 2X^2  0 X^2 2X^2 2X^2  0 2X^2  0  0  0 2X^2 2X^2  0  0 2X^2  0 2X^2 X^2 X^2 X^2 X^2  0 X^2 2X^2 X^2 2X^2
 0  0  0 X^2  0 X^2 2X^2 X^2 X^2  0  0 2X^2 2X^2 X^2  0  0 X^2 X^2 2X^2 X^2 2X^2 X^2 2X^2  0 X^2 2X^2 2X^2 X^2 2X^2  0  0 2X^2  0 2X^2 2X^2  0 X^2  0 2X^2 2X^2 2X^2  0  0 2X^2 2X^2  0 2X^2  0 2X^2  0 X^2 X^2 2X^2  0 X^2 X^2 X^2 2X^2 X^2  0 X^2 X^2 X^2 2X^2 2X^2 X^2 2X^2  0 X^2 X^2 2X^2 X^2 2X^2  0 X^2  0 X^2
 0  0  0  0 X^2 2X^2 X^2  0 X^2 X^2 X^2 2X^2  0 2X^2 X^2  0 2X^2 X^2  0 X^2 2X^2 2X^2 2X^2 2X^2 X^2 X^2  0  0  0 2X^2 X^2 X^2 2X^2 2X^2 2X^2  0  0  0  0 2X^2  0 X^2 2X^2 X^2 X^2  0 X^2 X^2  0 2X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0 2X^2 2X^2 X^2 2X^2 2X^2  0 2X^2 2X^2 2X^2 2X^2  0 2X^2 X^2 X^2  0 2X^2 X^2  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+70x^150+72x^153+1944x^154+54x^156+36x^159+8x^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 0.221 seconds.