The generator matrix

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

generates a code of length 34 over Z16 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+182x^28+176x^29+864x^30+1032x^31+2154x^32+2280x^33+2934x^34+2608x^35+2077x^36+864x^37+724x^38+200x^39+213x^40+8x^41+54x^42+13x^44

The gray image is a code over GF(2) with n=272, k=14 and d=112.
This code was found by Heurico 1.16 in 2.31 seconds.