The generator matrix

 1  0  1  1  1  4  1  1  6  1  1 10  1  1  1  1 10  1  0  1  4  1  0  1  0  1 12  4  1  1  1  2  4  1
 0  1  1  0 11  1 10  5  1  7  6  1  2  7  8 13  1 14  1  1  1 14  1  6  4  5  1 12  6 10  5  1  1  0
 0  0  2  6  4  6 14  4  0  6  4  6  6 10  4  0 12  8  4 14  2 12  2  6  2  2  4  2 10 14  6 10  2  0
 0  0  0 12  0  4  0 12  0  4  4  8  4  8  8  4  4  4 12  4  8  0 12  0 12  4  4  0 12  0  0  8  0  0
 0  0  0  0  8  0  0  0  0  0  8  8  8  8  0  8  8  8  0  8  0  0  8  0  0  0  0  8  8  8  0  0  0  0
 0  0  0  0  0  8  0  0  8  0  0  0  0  0  8  8  0  8  0  8  0  8  8  0  0  8  8  8  8  8  8  8  8  0
 0  0  0  0  0  0  8  0  0  8  0  0  8  8  0  8  0  0  8  8  0  8  0  0  8  8  8  0  0  8  8  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+55x^26+122x^27+407x^28+838x^29+2057x^30+3628x^31+8268x^32+10270x^33+14252x^34+10208x^35+8338x^36+3754x^37+2004x^38+740x^39+374x^40+106x^41+61x^42+22x^43+15x^44+8x^45+3x^46+5x^48

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 19.4 seconds.