The generator matrix

 1  1  1  1  1  1  1  1  1  1  2  2  2  1  1  2  2  4  4  4  2  1  2  2  1  4  1
 0  8  0  8  0  0  8  8  0  0  8  8  0  8  8  0  0  8  8  0  8  0  8  0  0  0  8
 0  0  8  8  0  8  8  0  0  8  8  0  8  8  0  8  0  8  0  8  8  0  0  0  8  0  8

generates a code of length 27 over Z16 who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+3x^26+50x^27+3x^28+1x^30+6x^31

The gray image is a code over GF(2) with n=216, k=6 and d=104.
This code was found by Heurico 1.16 in 0.0068 seconds.