The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+170x^26+172x^27+911x^28+984x^29+2530x^30+4100x^31+7762x^32+10148x^33+11932x^34+10032x^35+7995x^36+4128x^37+2610x^38+980x^39+657x^40+164x^41+190x^42+12x^43+46x^44+8x^46+4x^48

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 30.7 seconds.