The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+62x^12+234x^14+128x^15+648x^16+864x^17+2240x^18+1296x^19+810x^20+226x^21+36x^23+16x^24

The gray image is a code over GF(3) with n=81, k=8 and d=36.
This code was found by Heurico 1.16 in 0.0136 seconds.