The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+52x^29+489x^30+1376x^31+1994x^32+2978x^33+2774x^34+2970x^35+1937x^36+1162x^37+421x^38+132x^39+55x^40+30x^41+4x^42+2x^43+3x^44+2x^45+2x^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 1.2 seconds.