The generator matrix

 1  0  1  1  1  4  1 14  1  2  1  1  1 14  1 10  1 12  1  1  1  4  4  1  4  1  1  2  1  1  1
 0  1  1  0 11  1 14  1 15  1  5 10  4  1  7  1 14  4  1 15 11  2  1  9  1  6 10 12  6  2  8
 0  0  2  6  0  2  8  0 10  6  0  6  2  4 10  6  4  2  8  2  8  2  0  8  2  6  4  2  4  4  4
 0  0  0 12  0  4  0  0 12  4  8 12  4  0 12  8  4  8  4  0 12  8 12  4  4  0  4 12  0 12 12
 0  0  0  0 12  4  4 12  8  0  8  4  4  8  4  8 12  4  8  4  8  0  8  0  4  0  8 12  4 12  4
 0  0  0  0  0  8  0  8  8  8  0  8  0  8  0  8  0  8  8  0  0  8  0  8  0  8  8  0  8  0  8

generates a code of length 31 over Z16 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+81x^24+302x^25+813x^26+1590x^27+4162x^28+6908x^29+12353x^30+13024x^31+12333x^32+7146x^33+4297x^34+1462x^35+610x^36+232x^37+135x^38+52x^39+29x^40+4x^41+2x^42

The gray image is a code over GF(2) with n=248, k=16 and d=96.
This code was found by Heurico 1.16 in 18 seconds.