The generator matrix

 1  0  1  1  1  6  1 12  1 10  1  1  1  1  8 14  1  1  1 14  1  1  8  1  2  2 14  1  0  1  1  1  4  1
 0  1 11  6 13  1  2  1 12  1  3 13 15 14  1  1  9  0 11  1  6  8  1  6  1  1  1 15  1  0 11  6  2 13
 0  0 12  0  4  4  8  0  8 12  0  0  4 12 12  8  4 12  0  4 12  8  8  0  0  0  4  8  4  4 12  8  4  4
 0  0  0 12  0  4  4  0  0 12  8  4  4  8  8  4 12  4  4  8 12 12  4  0 12  8 12  0  4  0  0  8  0  8
 0  0  0  0  8  0  8  8  8  8  8  0  0  8  8  0  8  0  8  0  8  8  8  8  0  8  0  0  8  8  8  0  8  8

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

Homogenous weight enumerator: w(x)=1x^0+76x^29+210x^30+572x^31+1094x^32+1418x^33+1513x^34+1444x^35+1079x^36+466x^37+171x^38+92x^39+13x^40+22x^41+7x^42+4x^43+5x^44+2x^45+3x^46

The gray image is a code over GF(2) with n=272, k=13 and d=116.
This code was found by Heurico 1.16 in 1.54 seconds.