The generator matrix

 1  0  0  1  1  1 14  6  1  1  1 10  1 12  1  1  6  1  6  6  1  4 10  6  1  1  2 10 12  8  1
 0  1  0  0 13  1  1  6 13  9 12  1  6  1  2 15  8 15  1  1  8  1  1  1 10  2  1  1  1  1 10
 0  0  1  3  7  4  7  1 13 10  6  6  3  5 13  5  1  8  5 14  6  7  4  3 12  2 12  3  7  2 14
 0  0  0  8  8  0  8  8  0  8  8  8  0  0  8  0  0  8  8  0  0  8  8  0  8  0  0  0  0  8  8

generates a code of length 31 over Z16 who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+134x^27+580x^28+1268x^29+1406x^30+1712x^31+1299x^32+964x^33+464x^34+250x^35+77x^36+24x^37+10x^38+2x^40+1x^44

The gray image is a code over GF(2) with n=248, k=13 and d=108.
This code was found by Heurico 1.16 in 0.296 seconds.