The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+128x^26+28x^27+498x^28+428x^29+1190x^30+1980x^31+4217x^32+4748x^33+6396x^34+4724x^35+4146x^36+1956x^37+1308x^38+436x^39+386x^40+36x^41+124x^42+28x^44+6x^46+4x^48

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 8.89 seconds.