The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  3  1  3  3
 0  3  0  0  0  0  0  3  3  0  3  6  3  0  0  3  3  3
 0  0  3  0  0  0  0  6  3  6  6  0  3  0  3  6  0  3
 0  0  0  3  0  0  3  6  0  0  3  0  3  3  6  6  3  0
 0  0  0  0  3  0  6  6  0  6  3  6  0  3  3  3  3  3
 0  0  0  0  0  3  6  6  3  3  3  6  6  0  6  6  6  3

generates a code of length 18 over Z9 who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+104x^27+126x^30+450x^33+768x^36+558x^39+90x^42+72x^45+18x^48

The gray image is a code over GF(3) with n=54, k=7 and d=27.
This code was found by Heurico 1.16 in 3.01 seconds.