The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  0  1  6  1  6
 0  1  0  0  3  7  7  1  5  6  8  1  1  1  5  1
 0  0  1  1  5  6  2  4  7  7  8  5  1  3  0  7
 0  0  0  6  6  0  6  6  3  0  0  3  3  3  6  6

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

Homogenous weight enumerator: w(x)=1x^0+106x^27+432x^28+234x^30+324x^31+198x^33+486x^34+170x^36+216x^37+18x^39+2x^45

The gray image is a code over GF(3) with n=48, k=7 and d=27.
This code was found by Heurico 1.16 in 0.0315 seconds.