The generator matrix

 1  0  1  1  6  1  1  1  6  1 12  1  1  8  1  1 12  1  1  1  8  1  1  1  1  1  8  1  1  1  2 14  1  1
 0  1  1  6  1  3  5  4  1  2  1  7 13  1  6  4  1  1 10 12  1  3 14  4  3  1  4 11 13 12  0  1 10  1
 0  0  2  0  0  8  8 10  6 10 14 10  2  4 12 12  2 12 14 14  2 14  2  4  8  6  2 12 12  2  2 12  8  2
 0  0  0  8  0  8  0  0  8  8  0  0  8  8  8  8  8  0  8  0  0  8  0  0  8  0  8  0  8  8  8  8  0  8
 0  0  0  0  8  0  8  0  0  8  8  8  0  0  0  8  8  8  0  8  8  8  8  8  8  0  0  8  8  8  8  0  0  8

generates a code of length 34 over Z16 who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+431x^30+376x^31+1274x^32+1152x^33+1824x^34+1200x^35+1152x^36+320x^37+348x^38+24x^39+64x^40+20x^42+4x^44+1x^46+1x^48

The gray image is a code over GF(2) with n=272, k=13 and d=120.
This code was found by Heurico 1.16 in 58.5 seconds.