The generator matrix
1 1 1 3 1 1 1
0 3 24 3 0 0 0
0 0 9 0 0 9 0
0 0 0 18 0 9 0
0 0 0 0 9 18 0
generates a code of length 7 over Z27 who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+38x^6+102x^9+1130x^12+2916x^14+2158x^15+194x^18+22x^21
The gray image is a code over GF(3) with n=63, k=8 and d=18.
This code was found by Heurico 1.16 in 0.00445 seconds.