The generator matrix

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

generates a code of length 34 over Z16 who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+640x^29+2422x^30+4642x^31+7377x^32+11412x^33+12450x^34+11378x^35+7944x^36+4528x^37+1922x^38+606x^39+124x^40+60x^41+6x^42+14x^43+8x^44+2x^48

The gray image is a code over GF(2) with n=272, k=16 and d=116.
This code was found by Heurico 1.16 in 15.8 seconds.