The generator matrix

 1  0  0  1  1  1 10  4  2  0  1  1  1  1  1  2  4  1  1 14  1  0  6  1  1  1  1 10  8  1  1  0  0  1
 0  1  0  4  5  1  1  1  1  6 10  0 15 11  2  1  1  3 15  2  5  1  1  1  0  8  5  8  1  7  3  1  1  0
 0  0  1  7  3  4  3  2  1  1  5  6  3  2  2  4  7  5  0  1  6  5  3  1  5  4 13  1  7  7  9  0  8  0
 0  0  0  8  0  0  0  0  0  0  8  0  8  8  8  8  0  0  8  8  0  8  8  8  8  0  0  0  8  8  0  0  0  0
 0  0  0  0  8  0  0  0  0  0  8  8  8  8  0  8  8  0  0  8  8  0  0  8  0  8  0  8  8  8  8  8  0  0
 0  0  0  0  0  8  0  8  8  8  0  0  0  8  0  0  8  8  0  8  8  8  0  8  8  8  0  0  0  8  8  0  8  8

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

Homogenous weight enumerator: w(x)=1x^0+50x^28+434x^29+930x^30+2316x^31+3376x^32+6036x^33+6403x^34+6264x^35+3403x^36+2172x^37+845x^38+372x^39+79x^40+60x^41+13x^42+8x^43+3x^44+2x^45+1x^46

The gray image is a code over GF(2) with n=272, k=15 and d=112.
This code was found by Heurico 1.16 in 4.25 seconds.