The generator matrix

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

generates a code of length 34 over Z16 who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+61x^26+280x^27+583x^28+1288x^29+2649x^30+4416x^31+7173x^32+9762x^33+12770x^34+10120x^35+7441x^36+4346x^37+2449x^38+1280x^39+540x^40+214x^41+116x^42+32x^43+4x^44+6x^45+2x^46+1x^48+1x^50+1x^56

The gray image is a code over GF(2) with n=272, k=16 and d=104.
This code was found by Heurico 1.16 in 27.4 seconds.