The generator matrix

 1  0  1  1  1 14  1  1  6  1  8  1  1  1 12  2  1  1 10  0  1  1  1  4  1  1  6  1  1  1  8  1  1  1
 0  1 11 14  5  1  0  3  1  6  1  9 13  4  1  1  7 10  1  1  2 15  5  1 11 14  1  7  1 13  2  0  8  0
 0  0 12  4  0  4 12  0  8  8 12  0  4  4  0  4  4  8  0  0 12  0  0 12 12 12  8 12  4 12 12  0 12  0
 0  0  0  8  0  0  0  0  8  0  0  8  8  0  0  0  8  8  0  8  8  0  8  8  8  0  8  8  8  0  0  8  8  0
 0  0  0  0  8  0  0  0  0  8  8  0  8  8  0  8  8  8  0  8  8  0  0  8  0  8  8  8  0  0  8  8  0  8
 0  0  0  0  0  8  0  0  0  0  8  0  0  0  0  8  8  8  8  8  0  8  8  0  8  0  0  8  8  0  8  0  8  0
 0  0  0  0  0  0  8  0  8  0  0  8  8  8  8  8  0  0  8  8  8  0  0  8  0  8  0  8  8  0  0  0  8  8
 0  0  0  0  0  0  0  8  0  8  8  8  8  8  8  0  0  0  8  8  0  0  8  0  0  0  8  0  0  8  0  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+30x^26+56x^27+183x^28+234x^29+769x^30+2180x^31+3698x^32+6232x^33+6041x^34+6236x^35+3646x^36+2196x^37+794x^38+220x^39+138x^40+40x^41+40x^42+12x^43+11x^44+2x^45+5x^46+3x^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 5.34 seconds.