The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+156x^29+306x^30+698x^31+799x^32+1588x^33+1209x^34+1644x^35+712x^36+566x^37+210x^38+186x^39+72x^40+24x^41+18x^42+2x^45+1x^50

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 0.56 seconds.