The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+55x^26+172x^27+323x^28+532x^29+1053x^30+2042x^31+3247x^32+5400x^33+7046x^34+5546x^35+3202x^36+2078x^37+1122x^38+398x^39+248x^40+174x^41+67x^42+34x^43+19x^44+6x^45+1x^46+2x^49

The gray image is a code over GF(2) with n=272, k=15 and d=104.
This code was found by Heurico 1.16 in 9.07 seconds.