The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  1  2  4  2  2  4  2  0  1  1  1  2  4  1  1  1
 0 12  0  4  0  0  4 12  0  8  4  4  0 12 12  8  0  8  0  4  4 12 12 12  4  4  8  4  4 12  4 12  8  0
 0  0 12  4  0 12  4  0  8  4  0  4  0  4  8  4 12  4 12  4  4  0  8  0 12  0 12  4  0  8  4  4  8  0
 0  0  0  8  0  0  0  0  8  8  8  8  8  0  8  0  0  0  8  0  0  8  8  0  8  0  0  0  8  0  0  8  8  0
 0  0  0  0  8  0  0  0  0  0  0  8  8  8  0  0  8  0  8  8  8  8  8  0  8  8  0  8  8  0  0  0  0  0
 0  0  0  0  0  8  0  0  0  8  0  0  8  8  8  8  0  0  0  8  0  0  8  0  8  8  8  8  8  8  0  8  0  0
 0  0  0  0  0  0  8  0  8  8  8  8  8  0  8  8  8  0  8  8  8  0  0  8  8  8  8  0  8  8  8  0  0  8
 0  0  0  0  0  0  0  8  0  0  8  0  0  0  0  8  8  8  8  8  8  0  0  0  0  8  0  8  8  8  8  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+31x^26+52x^27+102x^28+166x^29+232x^30+582x^31+429x^32+2274x^33+519x^34+2270x^35+380x^36+590x^37+196x^38+162x^39+96x^40+38x^41+41x^42+6x^43+14x^44+4x^45+4x^46+2x^48+1x^50

The gray image is a code over GF(2) with n=272, k=13 and d=104.
This code was found by Heurico 1.16 in 0.713 seconds.