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

generates a code of length 42 over Z9[X]/(X^2+6,3X) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+234x^84+4x^90+4x^99

The gray image is a code over GF(3) with n=378, k=5 and d=252.
This code was found by Heurico 1.16 in 0.0169 seconds.