The generator matrix

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

generates a code of length 34 over Z16 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+48x^28+52x^29+164x^30+116x^31+668x^32+472x^33+1068x^34+472x^35+657x^36+116x^37+165x^38+52x^39+31x^40+5x^42+3x^44+3x^46+3x^50

The gray image is a code over GF(2) with n=272, k=12 and d=112.
This code was found by Heurico 1.16 in 0.175 seconds.