The generator matrix

 1  0  1  1  1 12  1  1  2  1 14  1 12  1  1  1  1  8  1  6 14  1  1  1  2  1  2  1 12  4  1  1  2  1
 0  1  1 12 11  1  2  7  1 14  1 13  1  8  3  5  5  1  8  1  1  7  6  3  1  6  4  1  1  1 15 10  4  0
 0  0  2  6  4  6  2 14  2  4  4  4  0 12  6  0  6  2  2  0  2  2  0  0 10  6  2 10  8  4  0 14  2  0
 0  0  0  8  0  0  0  0  0  0  8  8  0  8  8  0  0  8  8  8  8  8  0  0  0  8  0  0  8  0  0  8  8  0
 0  0  0  0  8  0  0  0  0  0  0  8  0  0  0  8  0  0  8  0  8  8  8  8  0  8  8  8  0  8  0  8  8  8
 0  0  0  0  0  8  0  0  8  0  0  0  0  0  0  8  8  8  0  8  8  8  0  8  0  8  8  0  8  0  8  8  0  0
 0  0  0  0  0  0  8  0  0  0  8  8  0  8  8  8  8  0  0  0  8  0  8  0  8  0  0  0  8  8  0  0  8  8
 0  0  0  0  0  0  0  8  8  8  0  0  8  0  8  8  8  0  8  0  0  8  0  0  0  8  8  0  0  8  0  0  0  8

generates a code of length 34 over Z16 who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+43x^26+138x^27+317x^28+746x^29+1792x^30+3998x^31+7134x^32+12998x^33+11152x^34+13106x^35+7125x^36+4026x^37+1786x^38+666x^39+256x^40+146x^41+69x^42+12x^43+13x^44+4x^45+6x^46+1x^48+1x^52

The gray image is a code over GF(2) with n=272, k=16 and d=104.
This code was found by Heurico 1.16 in 18.8 seconds.