The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+154x^24+200x^25+840x^26+1456x^27+3817x^28+7440x^29+11844x^30+13464x^31+12553x^32+7592x^33+3668x^34+1440x^35+756x^36+128x^37+92x^38+24x^39+60x^40+4x^42+3x^44

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 17.3 seconds.