The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  1  1  4  1  2  0  2  1  1  2  4  1  1  2  2  1  2  2  1
 0  2  0  2  0  0  2 10  6  4  4  6  6  4 10  8 12  2  2 10  8 10  2 14  0  2 14 14  6 14  8 10 12  0
 0  0  2  2  0 14  2  4  2  2  0  8 12  2 14  2  0  2 12 12  2  8 14  4 14 10 10 10 10  2 12  2  2  0
 0  0  0  4  0  0  0  0  0  0  8  8  8 12  4 12 12  0 12  4  8 12  0  8 12  4  4  4 12  0  4  0  8  0
 0  0  0  0 12  4  0  4  4  8 12  0 12  4  4  8  0  8  4  8  8 12  8  4  0  4 12  8  8  4  0  4 12  0
 0  0  0  0  0  8  8  0  8  8  8  8  8  8  0  8  8  0  8  0  8  0  0  0  8  8  8  0  0  8  8  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+35x^26+100x^27+405x^28+650x^29+1425x^30+1990x^31+3748x^32+4968x^33+6097x^34+4910x^35+3989x^36+2020x^37+1265x^38+594x^39+349x^40+104x^41+72x^42+22x^43+18x^44+2x^45+2x^46+2x^48

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 7.96 seconds.