The generator matrix

 1  0  1  1  1 10  1  1 14  1  1  6 10  1  1  4  2  1  1  1  6  1  1  1  1  1  1  1  8  1  1
 0  1  1  0  3  1  8 11  1 10  3  1  1 10 13  1  1  1  2  0  1  1  4  6  1  6  7  9  1  7  8
 0  0  2  0 14  8  2 12  2 14  4  6  4 10  0  4  6 10  0  8  0 14  4 12  4  8  6 10  0  2  8
 0  0  0  2 14 14 14  8  6  0 10  8  2 10 12 12 12 14 10  6  8  8 12  4 10  0  0  2  4  0  2

generates a code of length 31 over Z16 who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+96x^26+472x^27+980x^28+2016x^29+3072x^30+3266x^31+2999x^32+1994x^33+877x^34+380x^35+145x^36+52x^37+18x^38+10x^39+2x^40+2x^41+1x^42+1x^44

The gray image is a code over GF(2) with n=248, k=14 and d=104.
This code was found by Heurico 1.16 in 1.34 seconds.