The generator matrix

 1  0  1  1  1  4  1  1  2  1  1 14  0  1  1  1  1  4  1  1  2  1  6  2  1  1  1 10  1  1  1  6  8  1
 0  1  1  0 11  1 14 15  1  2  5  1  1  5  0  7  6  1 12  3 14 11  1  6  1  4  6  1  3 11 12  1  4  5
 0  0  2  6  0  2  8  2  6  2  0  4 12  4  4  6  0  6  6 12  6  6  6 14  8  0  2 10  8 14  2 14  8  0
 0  0  0 12  0  4  0  0 12  4  8  4  4  0  8  4  8  4  8  4  0  0  8 12  4 12  0  8  8 12  8  0  0 12
 0  0  0  0 12  4  4  4  0  4  8 12  8  4  4  0  0  8  0  8  4 12  8  8  8  0 12 12  0  8 12 12 12 12
 0  0  0  0  0  8  0  0  8  0  0  8  8  8  8  8  8  0  8  0  0  8  8  0  8  0  8  0  0  0  0  8  8  8

generates a code of length 34 over Z16 who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+144x^27+467x^28+900x^29+2024x^30+4248x^31+7408x^32+11210x^33+12957x^34+10828x^35+7415x^36+4518x^37+2113x^38+736x^39+315x^40+134x^41+55x^42+44x^43+10x^44+6x^45+3x^46

The gray image is a code over GF(2) with n=272, k=16 and d=108.
This code was found by Heurico 1.16 in 34.1 seconds.