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 2X  0 2X^2+X 2X 2X^2+X X^2+2X  0 X^2 2X^2+X 2X  0 X^2+X 2X^2+2X X^2 X^2+X 2X X^2 2X^2+X X^2 X^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 X^2+2X X^2+2X 2X  0 2X^2+X 2X 2X^2  X 2X^2+2X X^2 2X^2+2X  0  X 2X^2+X 2X^2+2X 2X^2 X^2+X 2X^2+2X 2X^2  X X^2+2X X^2 X^2+X 2X^2+2X  X 2X^2+2X X^2 2X^2 2X^2 2X^2 2X^2+X X^2+X  0 2X^2+2X 2X  X 2X^2+2X 2X^2  X  0
 0  0 X^2  0 2X^2 2X^2 X^2  0 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 X^2  0 2X^2 X^2 X^2 2X^2  0 2X^2  0 2X^2 2X^2  0 X^2 X^2 X^2 X^2  0  0 2X^2  0  0 X^2 2X^2 2X^2 2X^2 X^2 X^2 X^2 2X^2  0  0 2X^2 2X^2 X^2  0  0 2X^2  0 X^2 2X^2 2X^2  0 2X^2  0  0 2X^2  0
 0  0  0 X^2 X^2 2X^2 2X^2 X^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 X^2 2X^2 X^2 2X^2 2X^2  0  0  0 2X^2 2X^2 2X^2 X^2 X^2  0 2X^2 X^2 2X^2  0 X^2 X^2 X^2 X^2 X^2 2X^2  0  0 X^2 2X^2  0 2X^2  0 X^2 2X^2 X^2 2X^2 X^2 2X^2  0 X^2 2X^2 2X^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+12x^147+84x^149+100x^150+1782x^152+90x^153+72x^155+34x^156+6x^158+2x^159+2x^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 0.249 seconds.