The generator matrix

 1  0  0  1
 0  1  0 18
 0  0  1 18
 0  0  0 21

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

Homogenous weight enumerator: w(x)=1x^0+60x^2+8x^3+1350x^4+360x^5+16440x^6+5400x^7+114768x^8+32864x^9+5400x^10+480x^11+16x^12

The gray image is a code over GF(3) with n=36, k=11 and d=6.
This code was found by Heurico 1.16 in 0.318 seconds.