The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  2  4  2  2  2  8  1  4  1
 0 12  0  0  0  4 12  4  0  8  4 12  0  8 12  0  4  8  4 12 12  4  8 12  0 12 12  4  4  4  8 12  4  8
 0  0 12  0  4  4 12  0  0  0  4  8  4  4  0  8  4 12  0  8 12 12  4  8  0  8 12  8  0  4  4  4 12 12
 0  0  0 12  4  0 12  4  0  4 12  8 12  0  4  8  0 12 12  0  8  0  0  8 12  0 12 12 12  8 12  4  8  8
 0  0  0  0  8  0  0  0  8  0  8  8  0  0  0  0  0  8  8  0  8  0  8  8  8  8  0  8  0  0  0  8  0  0
 0  0  0  0  0  8  0  0  8  8  8  0  8  0  8  8  8  0  8  0  8  0  0  8  8  8  0  0  8  8  0  8  0  8
 0  0  0  0  0  0  8  0  0  0  0  0  0  8  8  8  8  0  8  0  8  0  8  8  0  8  8  8  0  0  0  8  0  8
 0  0  0  0  0  0  0  8  8  8  0  8  0  0  0  0  8  8  0  8  0  0  8  8  0  0  8  8  8  0  0  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+129x^26+8x^27+375x^28+72x^29+723x^30+440x^31+1900x^32+2552x^33+3980x^34+2552x^35+1976x^36+440x^37+656x^38+72x^39+328x^40+8x^41+139x^42+25x^44+5x^46+3x^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 23.7 seconds.