The generator matrix

 1  0  0  1  1  1 10  1 12  1  6  1  1  1 10  2  1 14  8  1  1  1  1  1  1 12  8  1 12  0 10  6  6  1
 0  1  0  4  5 11  1  2  1  4  0  8  9  5  1  2  7  1  1 11  6  0 15 15  8  6  1  9  1  6  2 14  0  4
 0  0  1  7  3  4  5  2  5  1  1 14  8  5  0  1  2  2  7  7  5  6  0  5  4  1 10  9  0  1  1  1  1  4
 0  0  0  8  0  0  0  0  0  0  8  8  8  0  0  8  0  8  8  8  8  8  8  0  8  8  0  8  8  0  8  0  0  0
 0  0  0  0  8  8  0  8  8  8  8  8  8  0  8  0  0  8  0  8  8  0  0  8  0  0  8  0  0  8  8  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+56x^29+651x^30+1076x^31+2144x^32+2444x^33+3839x^34+2394x^35+2050x^36+924x^37+585x^38+124x^39+58x^40+16x^41+13x^42+6x^43+2x^44+1x^48

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 1.11 seconds.