The generator matrix

 1  0  0  1  1  1  2  1  1  1  1  4  2  0  2  1  1  2  1  1 10  4  8  1  1  1  1 12  0 10  1  1  8  1
 0  1  0  2  5  7  1  0 14  9  7  1  1  6  2  4  3  1  3 12  0  1  1 15  1  1  6  1  1  1  0  1  1  4
 0  0  1  1  3  2  1  6  7  5  4  2  7  1  1  1  3  2  0  6  1  4  1  5  2  2  5  6  5  9 14  5  1  4
 0  0  0  8  0  0  0  0  8  8  8  0  0  8  0  0  8  8  0  8  8  8  0  0  0  8  8  0  8  0  8  0  0  0
 0  0  0  0  8  0  0  0  0  8  0  8  8  8  8  8  0  8  8  8  8  0  8  0  0  8  0  0  8  0  0  0  0  0
 0  0  0  0  0  8  0  0  0  0  8  8  8  8  8  0  0  0  8  0  0  0  0  8  0  8  8  8  0  8  8  0  0  8
 0  0  0  0  0  0  8  8  8  0  0  0  8  8  0  8  0  0  0  8  8  0  0  8  0  8  0  8  8  8  8  8  0  0

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

Homogenous weight enumerator: w(x)=1x^0+28x^27+252x^28+740x^29+1873x^30+4152x^31+7170x^32+12262x^33+12703x^34+12132x^35+7155x^36+4330x^37+1763x^38+576x^39+265x^40+74x^41+43x^42+8x^43+5x^44+2x^45+2x^50

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 15.9 seconds.