The generator matrix

 1  1  1  1  1  1  1  1  1  1
 0  3  0 21  0  3 24 15 24  0
 0  0  3  6 24  3  0 21 24  0
 0  0  0  9  0 18  0  9 18  0
 0  0  0  0  9  9 18  9  9  0

generates a code of length 10 over Z27 who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+92x^12+144x^14+336x^15+864x^17+480x^18+15336x^20+608x^21+1152x^23+636x^24+32x^27+2x^30

The gray image is a code over GF(3) with n=90, k=9 and d=36.
This code was found by Heurico 1.16 in 0.0974 seconds.