The generator matrix

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

generates a code of length 34 over Z16 who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+144x^26+16x^27+559x^28+272x^29+1638x^30+1648x^31+4619x^32+4208x^33+6597x^34+4208x^35+4570x^36+1648x^37+1708x^38+272x^39+456x^40+16x^41+146x^42+31x^44+6x^46+4x^48+1x^50

The gray image is a code over GF(2) with n=272, k=15 and d=104.
This code was found by Heurico 1.16 in 18.1 seconds.