The generator matrix

 1  0  0  0  1  1  1  1  1
 0  1  0  0 15 19 21 22 17
 0  0  1  0 16 19 22 15 20
 0  0  0  1 14 21 15 16 17

generates a code of length 9 over Z27 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 29.5 seconds.