The generator matrix

 1  0  1  1  1 14  1 12  1 10  1  1 10  1  1  1  8  1  2  8  1  1  1  1 14 12  2  1  2  1  1  1  4  2
 0  1  1  6  7  1  3  1  4  1 14  5  1  5  6  1  1 10  1  1  0 11 11 14  1  2  6  8  6  9 14  1  1 10
 0  0  2  0 14  8  0  2  6 10  2  4  6 10  8  0  0 14  4  2  4  8 12  4 14 14  6 10  6  2 10  8 12  2
 0  0  0 12  0 12  8  4  4  4  8  4  0 12  8  0  4  8  0  8  4  4  8  8 12  0  0  0 12  0  4  4  0  4
 0  0  0  0  8  0  0  8  8  0  8  0  8  8  8  8  8  0  8  0  8  8  8  0  8  8  0  8  8  8  8  8  8  0

generates a code of length 34 over Z16 who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+280x^29+556x^30+1216x^31+1810x^32+2974x^33+2739x^34+3052x^35+1810x^36+1166x^37+410x^38+232x^39+87x^40+26x^41+7x^42+12x^43+4x^44+2x^45

The gray image is a code over GF(2) with n=272, k=14 and d=116.
This code was found by Heurico 1.16 in 8.5 seconds.