The generator matrix

 1  0  1  1  1  6  1  1  0  1  1 14  1  1  8  1  6  1 14  1  1  2  1  1  8  1 14  1  1  0  4  1  1  1
 0  1 11  6  1  1  8  5  1  3  0  1  7  6  1 13  1 14  1  3  3  0  8  8  1  1  1  2  9  1  2 12  6  8
 0  0 12  0  0  0  0  0  0  0  0  8  8  4 12 12 12  4  4 12  4  8  0  8 12 12  8 12  8 12  8  4 12  4
 0  0  0 12  0  0  0  0  4  4 12 12  4 12  4  4 12  4  4  8  4 12  4  0  8  0 12  4 12 12 12  4 12  0
 0  0  0  0  4  0  8  4  0  4  8  0 12 12 12  8 12  4  4  0  8 12  0  8  4 12 12  8  0  0  0  0 12  0
 0  0  0  0  0 12 12  4 12  8 12  0  4  4  0  4 12  0  8  4  0  8  4 12  4 12  4 12  4  8  8  0 12  0

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

Homogenous weight enumerator: w(x)=1x^0+138x^26+24x^27+583x^28+416x^29+1932x^30+3344x^31+7987x^32+11532x^33+13500x^34+11692x^35+8107x^36+3256x^37+1888x^38+424x^39+492x^40+28x^41+138x^42+4x^43+45x^44+4x^46+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 22.1 seconds.