The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  1  0  6  1  1 12  1  1  0  1  1 10  6  1  1  2  6  1  1  2  1
 0  1  3  6  5  1 12  7  1 10  9  1  0  3  1  1  6  5  1 12 15  1  9 10  1  1  0  6  6  1  3  0  0  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  8  8  0  0  8  0  0  0  8  0  8  0
 0  0  0  8  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  0  0  0  0  0  8  8  8  0  0  8  0  0  8  0
 0  0  0  0  8  0  0  0  0  8  8  8  0  8  8  8  0  0  8  8  0  8  0  8  8  8  8  0  8  8  8  0  0  0
 0  0  0  0  0  8  0  0  8  8  0  8  0  0  8  0  8  8  8  0  8  8  0  0  8  0  0  8  0  8  8  8  0  0
 0  0  0  0  0  0  8  0  8  0  0  8  8  0  0  8  8  0  8  8  0  0  0  0  0  8  0  8  8  8  8  0  8  0
 0  0  0  0  0  0  0  8  8  8  8  0  0  0  0  8  8  8  8  0  0  8  8  0  0  0  8  8  8  8  0  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+29x^26+16x^27+131x^28+94x^29+559x^30+750x^31+2529x^32+1942x^33+4270x^34+1974x^35+2559x^36+762x^37+490x^38+74x^39+140x^40+18x^41+21x^42+2x^43+13x^44+7x^46+2x^48+1x^52

The gray image is a code over GF(2) with n=272, k=14 and d=104.
This code was found by Heurico 1.16 in 1.34 seconds.