The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+170x^28+280x^29+598x^30+904x^31+1911x^32+2424x^33+3904x^34+2400x^35+1913x^36+856x^37+512x^38+280x^39+152x^40+24x^41+40x^42+12x^44+2x^46+1x^52

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 2.26 seconds.