The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+39x^26+142x^27+303x^28+660x^29+1253x^30+2014x^31+3490x^32+5370x^33+6221x^34+5418x^35+3556x^36+2002x^37+1136x^38+602x^39+316x^40+158x^41+51x^42+16x^43+13x^44+2x^45+3x^46+1x^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 7.66 seconds.