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

generates a code of length 42 over Z9[X]/(X^2+6,3X) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+62x^81+234x^82+126x^84+180x^85+30x^87+72x^88+18x^90+6x^96

The gray image is a code over GF(3) with n=378, k=6 and d=243.
This code was found by Heurico 1.16 in 0.0244 seconds.