The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+50x^24+368x^25+849x^26+1690x^27+4083x^28+7424x^29+11840x^30+12748x^31+12040x^32+7496x^33+4155x^34+1692x^35+637x^36+288x^37+111x^38+28x^39+21x^40+8x^41+4x^42+2x^43+1x^46

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 17.2 seconds.