The generator matrix

 1  0  0  1  1  1 10  2  1  1  1 14  1  8  1  1 14  0  1 12  1 10  1  4  1 10  2  1  1  1  1  1  1  1
 0  1  0  8  5 13  1  1 14 11 12 12  3  1  6  9  1  6  4  1 15  1  2  1  3  2  1  8  9 10 12 12  7 14
 0  0  1 11  3  8 15  2 15  7  2  1 10 13 13 14 12  1  9 10 13 13  4 15 12  1  8 15  1  0  8 14 10 11

generates a code of length 34 over Z16 who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+270x^31+856x^32+654x^33+942x^34+374x^35+538x^36+226x^37+144x^38+60x^39+13x^40+16x^41+2x^42

The gray image is a code over GF(2) with n=272, k=12 and d=124.
This code was found by Heurico 1.16 in 0.093 seconds.