The generator matrix

 1  0  1  1  1 14  1  4  1 10  1  1 14  1  1  0  1  1  1 12  1  1  1  1  1  6  1  1  1  1  1  2  2  1
 0  1  1  6  3  1 13  1  4  1 10 15  1  4  5  1  2  3 12  1  6 15 13  6  2  1 13 12 13  3  0  6 14 15
 0  0  2  0  8  8  0 14  6 14  6 10 12  4  6 12  6 12 14  6  4  0 14  8  0 12 10  2 12  0  8  6  6  6
 0  0  0 12  0  4  4 12  4  8  8  4 12  0  0  8  4 12  0  8  4  8  4  4  0  0 12  4  8 12 12 12  4  0

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

Homogenous weight enumerator: w(x)=1x^0+324x^30+652x^31+988x^32+1448x^33+1510x^34+1380x^35+1002x^36+540x^37+188x^38+64x^39+66x^40+12x^41+10x^42+6x^44+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 22 seconds.