The generator matrix

 1  0  1  1  1 14  1  1  0  1 14  1  1  6  1  1  1 12  8  1  1  1  1  1  1  4  2  1  2  2  0  0  1  2
 0  1 11  6  5  1 11  0  1  5  1  6 13  1  8  6  1  1  1  3  1  4 15  2 15  1  4  9  4  1  1  1 14  4
 0  0 12  0  0  0  0  4  4 12 12  0  8  8  8  4 12  4  0  4  0 12  8 12  4  0  8  0  8  4  8  4  0  0
 0  0  0 12  0  4  4  4 12 12  8  0  4  8  4  4  0 12  4 12 12  8  0  0  4  4 12  8  4  0  0 12  4 12
 0  0  0  0  8  0  0  0  0  0  8  0  8  0  0  0  8  8  8  0  0  0  8  8  8  8  0  8  8  8  8  0  0  8
 0  0  0  0  0  8  0  0  0  8  0  0  8  0  0  8  8  8  8  0  8  8  8  0  0  8  8  0  0  8  0  8  0  0
 0  0  0  0  0  0  8  0  8  0  0  8  0  8  8  0  0  8  8  0  0  8  8  0  8  8  8  0  0  0  8  8  0  0
 0  0  0  0  0  0  0  8  0  0  0  8  0  8  8  8  8  8  0  0  8  0  8  8  8  8  0  8  8  0  8  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+136x^26+92x^27+504x^28+528x^29+1989x^30+3380x^31+8041x^32+11356x^33+13353x^34+11340x^35+8356x^36+3420x^37+1803x^38+540x^39+468x^40+52x^41+118x^42+8x^43+36x^44+4x^45+7x^46+2x^48+1x^50+1x^54

The gray image is a code over GF(2) with n=272, k=16 and d=104.
This code was found by Heurico 1.16 in 21.1 seconds.