The generator matrix

 1  0  1  1  1 14  1  1  0  1 14  1  1  6  1  1  1  0  6  1  1  8  1  1  4  2  8  1  1  1  1  1  8  1
 0  1 11  6  1  1  0  3  1  5  1 14  5  1  8  9 14  1  1  0 13  1 12 11  1  1  4  2  0  3 15  6  2  8
 0  0 12  0  0  0 12  0  4 12 12  0  8  4  0  4  4  4  8 12  0 12 12  4  8  4  4  4  8  4  4 12  0  4
 0  0  0 12  0  0  0  0  0  0  0  8  0  8  8  8 12  4  4 12  4 12 12  8  4 12  8 12  0 12  4  8  0 12
 0  0  0  0  4  4  0  8 12  4  0 12  8 12  4 12  4  8  4  0  0 12  0  8  0 12  0 12  0  8  0  4 12 12
 0  0  0  0  0  8  0  0  8  8  8  0  8  0  8  0  8  0  8  8  0  0  0  8  0  0  0  8  8  0  8  8  0  0
 0  0  0  0  0  0  8  8  8  0  0  8  0  0  0  8  8  8  0  0  8  0  8  8  0  8  0  0  8  8  8  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+134x^26+44x^27+534x^28+524x^29+2156x^30+3604x^31+8251x^32+11212x^33+12670x^34+11100x^35+8230x^36+3716x^37+2254x^38+476x^39+420x^40+36x^41+124x^42+8x^43+35x^44+6x^46+1x^60

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 21.3 seconds.