The generator matrix

 1  0  0  0  1  1  1  1  1
 0  1  0  0 2X+6  7 X+6 X+7 X+8
 0  0  1  0 2X+7  7 X+7 2X+6 2X+8
 0  0  0  1 2X+5 X+6 2X+6 2X+7 X+8

generates a code of length 9 over Z9[X]/(X^2+6,3X) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+1812x^12+120x^13+8820x^14+10378x^15+75888x^16+34344x^17+199562x^18+151776x^19+34452x^20+13980x^21+150x^22+144x^23+14x^24

The gray image is a code over GF(3) with n=81, k=12 and d=36.
This code was found by Heurico 1.16 in 30.4 seconds.