The generator matrix

 1  1  1  1  1  1  1  1  2  0  1  2 12  1  1  1  2  8  2  4  1  1  1  1  2  2  1
 0  2 12  6  8 14  4 10  6  2  0 10  2 12  6 10 14  2  2  2  8  4 14  2  0 12 12

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

Homogenous weight enumerator: w(x)=1x^0+18x^26+88x^27+10x^28+8x^29+1x^32+2x^34

The gray image is a code over GF(2) with n=216, k=7 and d=104.
This code was found by Heurico 1.16 in 0.00494 seconds.