The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 12  8  2  2  1  1  0  1  2  0  1  8  4  1  1  2  2  1  1
 0  2  0  2  0  8  2 10  8  2 12 14  0 10  0  2  2 10 10 12 14 12 10  0  2  2  2  2 10  4 14  8  2  0
 0  0  2  2 12 14  6 12  0  2 10 12  4 14  2  6  0  6  8  6 10  2  4  6  2 12 12  4 10  6  0 14  0  0
 0  0  0  4  0  0 12  8  4  8 12 12 12  8  4  0 12  8  0  4 12  4 12  8 12  0  8  0  4  0 12  0 12  0
 0  0  0  0  8  8  8  8  0  0  0  8  8  8  8  8  8  0  8  0  0  0  0  8  8  8  0  0  8  8  8  8  0  0

generates a code of length 34 over Z16 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+44x^28+164x^29+373x^30+594x^31+886x^32+1478x^33+1253x^34+1392x^35+872x^36+538x^37+350x^38+130x^39+49x^40+42x^41+5x^42+12x^43+2x^44+2x^45+3x^46+2x^48

The gray image is a code over GF(2) with n=272, k=13 and d=112.
This code was found by Heurico 1.16 in 0.543 seconds.