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

generates a code of length 79 over Z3[X]/(X^3) who´s minimum homogenous weight is 156.

Homogenous weight enumerator: w(x)=1x^0+106x^156+1944x^158+108x^159+26x^162+2x^237

The gray image is a linear code over GF(3) with n=711, k=7 and d=468.
This code was found by Heurico 1.16 in 0.238 seconds.