The generator matrix

 1  0  1  1  4  1 10  1  1  1  1  6 10  1  1  1  1 14  1  1  1  1  8  1  0  2  1  2  1  1  1  1  0  0
 0  1  1  6  1  7  1  4 15  2  5  1  1  8  3 11  2  1 14 12  8  5  1  4  1 14  2  8  5  8 15 10  1  1
 0  0  2  0 10  2  6 10  8 10  8  0 10 14  6 12  4 12 10  6  0  6 12 12 14  6  6 14  4  2  8  8  2  0
 0  0  0  8  0  8  8  8  8  0  0  8  8  8  8  8  8  8  8  0  8  8  8  0  8  8  0  0  0  8  0  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+89x^30+344x^31+561x^32+704x^33+876x^34+618x^35+453x^36+258x^37+102x^38+42x^39+24x^40+14x^41+4x^42+4x^43+1x^44+1x^46

The gray image is a code over GF(2) with n=272, k=12 and d=120.
This code was found by Heurico 1.16 in 0.118 seconds.