The generator matrix

 1  0  1  1  1  1  1  0  1  1  1  1  1  1  1  1
 0  1  1  8  0  7  8  1  0  7  3  7  8  2  6  2
 0  0  6  0  3  6  3  0  6  3  6  0  0  3  6  0
 0  0  0  3  3  6  6  3  0  0  3  6  0  3  3  3

generates a code of length 16 over Z9 who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+44x^27+102x^28+60x^30+144x^31+88x^33+216x^34+38x^36+24x^37+8x^42+4x^45

The gray image is a code over GF(3) with n=48, k=6 and d=27.
This code was found by Heurico 1.16 in 0.00298 seconds.