The generator matrix

 1  0  1  1  1 14  1  1 14  1  0  1  1  6  1  1  1  1  1  8  1 12  1  1 12  1  1  4  1  1  1  2  2  1
 0  1 11  6  5  1 11  0  1 14  1 13  6  1  8  3  5  1 10  1  6  1  3  9  1  6  4  1  9  6 11  0  8  0
 0  0 12  0  0  0  0  4  4  4  4  4  4  8  0  8 12  8  0  4  4  4  4  0  4  8  8  4  8  0  8  4  4  0
 0  0  0 12  0  4  4  4  8  8 12  8  4  8 12  0  4 12  8  0  4  4 12  8 12  0 12  0  0  0 12  4  0  0
 0  0  0  0  8  0  0  8  8  8  8  8  8  8  8  8  8  8  8  8  0  8  8  8  0  8  0  0  8  0  8  8  0  0
 0  0  0  0  0  8  0  0  0  8  0  0  8  8  8  8  0  0  8  8  0  0  8  8  8  0  8  8  8  8  0  8  0  0
 0  0  0  0  0  0  8  0  0  0  0  8  0  8  8  0  8  8  0  8  0  8  0  8  8  0  8  0  0  8  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+47x^26+66x^27+237x^28+378x^29+790x^30+2308x^31+3062x^32+6458x^33+6075x^34+6472x^35+3080x^36+2318x^37+772x^38+364x^39+192x^40+62x^41+53x^42+6x^43+19x^44+6x^46+1x^48+1x^50

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 5.47 seconds.