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  X  X  1  1  1  X  X  1  1  1  1  1  X  X  1  1  1  1  X  X  X  1  X  3  3  0  X  X  X  1  1  X  3  X  3  0  3  1  1
 0  3  6  0  3  6  0  3  6  0  3  6  0  3  6  0  3  6  0  3  6  0  3  6  0  3  6  0  3  6  0  3  6  0  3  6  0  3  6  3  6  0  3  6  3  6  0  3  6  0  3  3  6  6  0  3  6  3  6  0  0  0  3  6  3  3  6  0  3  6  0  3  3  6  3  0  0  0

generates a code of length 78 over Z9[X]/(X^2+6,3X) who´s minimum homogenous weight is 157.

Homogenous weight enumerator: w(x)=1x^0+66x^157+2x^159+6x^160+4x^165+2x^168

The gray image is a code over GF(3) with n=702, k=4 and d=471.
This code was found by Heurico 1.16 in 0.177 seconds.