The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  3  1  1  1
 0  9  0  0  0  0  0  0  9  9  9  9  0 18  0  0
 0  0  9  0  0  0  0  9 18  9 18  9  9  9  0  0
 0  0  0  9  0  0  0 18 18  0  9  9  0  9  0  0
 0  0  0  0  9  0  0 18 18  9  0 18  0 18  0  0
 0  0  0  0  0  9  0 18 18 18  0  0  9  9  0  0
 0  0  0  0  0  0  9 18  9  9 18  0  0  9  0  0

generates a code of length 16 over Z27 who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+132x^18+44x^21+174x^24+308x^27+1698x^30+13122x^32+3486x^33+252x^36+198x^39+228x^42+36x^45+4x^48

The gray image is a code over GF(3) with n=144, k=9 and d=54.
This code was found by Heurico 1.16 in 0.258 seconds.