The generator matrix

 1  0  1  1  1  6  1 12  1  1  1 14  2  1  1  1  1  8  1  1  1 14  1  1  1  1  2  1  1  2  1  6  1  1
 0  1 11  6 13  1 12  1  3  5 14  1  1 10  7  9  8  1  4  1  2  1  4 10  6  0 14 10  2  8  9  1  3  0
 0  0 12  0  4  0  0  8  0  8  4 12 12  0  4  8  4  4 12 12  4  4 12  8  8  0 12  0  4 12  0  0  8  0
 0  0  0  8  0  0  8  0  0  0  0  0  0  8  8  8  8  8  0  8  8  8  8  8  0  0  8  8  0  0  0  0  8  0
 0  0  0  0  8  0  8  8  8  8  0  8  0  0  8  0  8  8  8  0  0  0  0  8  0  8  0  8  0  8  0  0  8  0
 0  0  0  0  0  8  0  8  8  0  0  0  8  8  0  0  8  8  0  8  8  8  0  0  8  0  0  8  8  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+25x^28+138x^29+194x^30+618x^31+786x^32+1698x^33+1322x^34+1684x^35+810x^36+582x^37+136x^38+116x^39+40x^40+14x^41+10x^42+12x^43+1x^44+2x^46+2x^47+1x^48

The gray image is a code over GF(2) with n=272, k=13 and d=112.
This code was found by Heurico 1.16 in 0.382 seconds.