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

generates a code of length 76 over Z3[X]/(X^3) who´s minimum homogenous weight is 147.

Homogenous weight enumerator: w(x)=1x^0+40x^147+84x^150+1944x^152+54x^153+48x^156+6x^159+8x^162+2x^228

The gray image is a linear code over GF(3) with n=684, k=7 and d=441.
This code was found by Heurico 1.16 in 0.213 seconds.