The generator matrix

 1  0  1  1  1  4  1  0  1  1  0  1  1 14  1  1  1  1  1  2  1  8  2  8  1  2  1 14 10  2 14  1  1  1
 0  1  1  0 11  1  9  1  8  7  1  4 14  1  7  1  2  2  9  0  5  1 12  2  9 10 12  1  1  0  1 12  4  4
 0  0  2  0  0  0  8  2  6  2  6 10  4  2  4  0  4 14 14  2 10  6 10  8  4 12 14  4  0  2  8  6  4  8
 0  0  0  2  4  2 14  2  2 14  8  8  8 14  6 12 14 10  8  4 10  4  6  6  2 10 14  6  4  8  6  4 14 10
 0  0  0  0  8  0  8  8  8  0  8  8  0  8  8  8  0  8  0  0  0  8  0  8  0  8  0  0  0  8  8  8  8  8
 0  0  0  0  0  8  8  8  0  8  0  8  8  0  0  8  8  8  8  8  0  8  0  0  8  8  8  8  8  8  0  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+40x^27+511x^28+884x^29+2376x^30+4028x^31+8096x^32+10284x^33+12698x^34+10580x^35+8427x^36+4108x^37+2244x^38+708x^39+390x^40+84x^41+58x^42+4x^43+14x^44+1x^56

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 19.9 seconds.