The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+39x^26+56x^27+157x^28+298x^29+401x^30+1378x^31+1519x^32+3354x^33+1950x^34+3426x^35+1498x^36+1422x^37+378x^38+246x^39+132x^40+46x^41+43x^42+14x^43+17x^44+5x^46+4x^48

The gray image is a code over GF(2) with n=272, k=14 and d=104.
This code was found by Heurico 1.16 in 2.32 seconds.