The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+256x^27+625x^28+1418x^29+2533x^30+4748x^31+6791x^32+10522x^33+11262x^34+11050x^35+7095x^36+4792x^37+2225x^38+1250x^39+610x^40+234x^41+76x^42+22x^43+14x^44+10x^45+2x^47

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 29.5 seconds.