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

generates a code of length 39 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+234x^78+2x^81+6x^90

The gray image is a code over GF(3) with n=351, k=5 and d=234.
This code was found by Heurico 1.16 in 0.0128 seconds.