The generator matrix

 1  0  0  1
 0  1  0 15
 0  0  1 15
 0  0  0 16

generates a code of length 4 over Z27 who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+96x^2+8x^3+3456x^4+576x^5+55320x^6+13824x^7+332928x^8+110624x^9+13824x^10+768x^11+16x^12

The gray image is a code over GF(3) with n=36, k=12 and d=6.
This code was found by Heurico 1.16 in 2.57 seconds.