The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  4  2  2  2  4  4  2  1  2  2  1  1  2  1  1
 0 12  0  0  0  4 12  4  8  0  4  0  8  4  4  4  4  8  4  4 12  4 12  4  8  8  0 12  4  8  0  4 12  0
 0  0 12  0  4  4 12  0  0  4  8  0 12 12  8  4  4  8 12  4  8  4  0  8  0 12  0  4  8  4  4  8  0  0
 0  0  0 12  4  0 12  4  4  8  0  8  4  4  4  8  8 12  8  8  8  8  0  4  4  0 12  4  4 12  0  8  0  0
 0  0  0  0  8  0  0  8  0  8  8  0  0  0  0  8  0  8  0  0  0  8  8  8  8  8  8  0  0  0  0  8  0  0
 0  0  0  0  0  8  0  8  8  8  0  8  8  0  8  8  0  0  8  0  0  0  0  0  8  0  8  8  8  8  8  8  0  0
 0  0  0  0  0  0  8  0  8  8  8  0  0  0  0  0  0  8  8  8  0  8  0  0  8  0  8  8  8  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+31x^26+72x^27+124x^28+188x^29+225x^30+348x^31+783x^32+1428x^33+1807x^34+1464x^35+755x^36+376x^37+199x^38+140x^39+115x^40+52x^41+38x^42+24x^43+13x^44+4x^45+4x^46+1x^48

The gray image is a code over GF(2) with n=272, k=13 and d=104.
This code was found by Heurico 1.16 in 0.699 seconds.