The generator matrix

 1  1  1  1  1  3  1
 0  3 24  0 21 21 24
 0  0  9  0  9 18  0
 0  0  0  9 18 18  0

generates a code of length 7 over Z27 who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+14x^9+54x^10+236x^12+216x^13+972x^14+456x^15+216x^16+18x^18+4x^21

The gray image is a code over GF(3) with n=63, k=7 and d=27.
This code was found by Heurico 1.16 in 0.00124 seconds.