The generator matrix

 1  1  1  1  1  1  1  1
 0  9  0  0  9  0  9  9
 0  0  9  0 18  9 18  9
 0  0  0  9 18 18  0 18

generates a code of length 8 over Z27 who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+20x^12+32x^15+648x^16+8x^18+16x^21+4x^24

The gray image is a code over GF(3) with n=72, k=6 and d=36.
This code was found by Heurico 1.16 in 0.000411 seconds.