The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+130x^30+272x^31+538x^32+848x^33+620x^34+768x^35+507x^36+272x^37+90x^38+16x^39+20x^40+8x^42+4x^44+1x^48+1x^52

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 0.149 seconds.