The generator matrix
1 0 0 1 1 1 1 1 1
0 1 0 1 15 19 17 15 18
0 0 1 26 16 22 18 16 22
0 0 0 24 18 9 12 6 3
generates a code of length 9 over Z27 who´s minimum homogenous weight is 12.
Homogenous weight enumerator: w(x)=1x^0+654x^12+144x^13+3096x^14+3432x^15+23220x^16+11448x^17+72096x^18+46440x^19+11556x^20+4728x^21+180x^22+144x^23+6x^24+2x^27
The gray image is a code over GF(3) with n=81, k=11 and d=36.
This code was found by Heurico 1.16 in 3.57 seconds.