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 X+3 2X X+3 2X+6  0  6 X+3 2X  0 X+6 2X+3  6 X+6 2X  6 X+3  6 2X+6 X+6 2X+6  3 X+6 2X+6  0  0  6  6 X+3 X+3 X+6 X+6 2X 2X+6 2X+6 2X  0 X+3 2X  3  X 2X+3  6 2X+3  0  X X+3 2X+3  3 X+6 2X+3  3  X 2X+6  6 X+6 2X+3  X 2X+3  6  3  3  3 X+3 X+6  0 2X+3 2X  X 2X+3  3  X  0
 0  0  6  0  3  3  6  0  6  3  3  0  6  0  6  6  0  6  3  6  0  3  6  0  3  3  3  0  6  6  0  3  6  6  3  0  3  0  3  3  0  6  6  6  6  0  0  3  0  0  6  3  3  3  6  6  6  3  0  0  3  3  6  0  0  3  0  6  3  3  0  3  0  0  3  0
 0  0  0  6  6  3  3  6  3  6  3  3  0  3  3  6  6  6  3  6  3  6  0  0  0  0  0  3  6  0  0  0  0  6  3  6  3  3  0  0  0  3  3  3  6  6  0  3  6  3  0  6  6  6  6  6  3  0  0  6  3  0  3  0  6  3  6  3  6  3  0  6  3  3  0  0

generates a code of length 76 over Z9[X]/(X^2+3,3X) 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 code over GF(3) with n=684, k=7 and d=441.
This code was found by Heurico 1.16 in 0.248 seconds.