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  6  1  1  1  1  1  1  1  1
 0  X 2X  0 X+3 2X 2X+6  6 X+3 X+3  0 2X X+3  0 2X 2X+6  3 X+6 X+3  0  6 X+6  0 X+3 2X 2X+6 2X+6 2X+3  6 X+6  6 X+6  6  0  3  6  0  6  6 X+6 X+6  X X+3 X+6 X+6 2X 2X+6 2X 2X+6 2X+6 2X 2X+6  0 2X 2X 2X+6 2X+6  0 X+3 X+6 X+6  X X+3 X+3 2X 2X+3 X+6  6 2X+3 X+3 2X+3  X 2X+6  6  X 2X
 0  0  6  0  0  0  3  0  3  6  0  6  6  6  0  6  6  0  3  3  6  0  3  6  6  0  3  3  3  6  6  3  3  0  0  3  3  6  6  0  3  3  3  6  3  0  3  0  0  6  6  3  3  0  6  3  0  0  3  0  6  0  6  3  3  3  0  0  0  6  6  6  6  6  0  0
 0  0  0  6  0  6  3  3  3  6  0  3  0  3  3  3  0  3  0  0  3  6  3  0  6  0  0  6  6  3  6  6  6  6  3  0  3  0  6  6  3  0  6  6  3  0  3  3  0  3  0  0  0  6  6  0  3  6  6  3  6  3  3  0  6  6  0  0  6  3  0  0  6  3  6  0
 0  0  0  0  3  3  6  0  3  6  3  3  0  0  3  0  6  0  3  3  6  0  3  6  0  3  6  6  3  6  6  3  6  3  3  6  6  0  0  6  0  0  6  3  6  0  0  0  6  6  3  3  0  0  6  0  6  6  0  6  0  3  3  6  3  0  6  0  6  0  6  3  3  3  3  0

generates a code of length 76 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+166x^144+528x^147+2148x^150+3120x^153+240x^156+78x^159+32x^162+204x^165+42x^168+2x^225

The gray image is a code over GF(3) with n=684, k=8 and d=432.
This code was found by Heurico 1.16 in 0.527 seconds.