The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  8  2  0 12  2  1  1  2  1  1 12  2  2  1  2  1  1  2
 0  2  0  2  0  4  6  6  4 12 10  6  4  2 10  0 12 14 14  2 14  8 12  2 12  0  4  2 12  8  4
 0  0  2  2  0  2 10  0  8  2 14  4  6  8  2  2  2  2  4 10  6 14 12  0  6  2 12  2  0 12  2
 0  0  0  4  0  0  4  0  0  0 12  0  0  4  8  8  8  8  4  8 12  4  4  4  0  4  0 12 12  4  4
 0  0  0  0 12  0  0  8  4  4 12  4 12  8  4  0 12  0 12  0  8  0  0  4  8  8 12 12  8 12  4
 0  0  0  0  0  8  8  8  8  8  8  8  0  8  0  0  0  0  0  8  8  8  0  0  8  0  0  0  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+147x^24+148x^25+808x^26+852x^27+2099x^28+3644x^29+5131x^30+7036x^31+5154x^32+3756x^33+2187x^34+812x^35+639x^36+132x^37+185x^38+4x^39+22x^40+9x^42+2x^44

The gray image is a code over GF(2) with n=248, k=15 and d=96.
This code was found by Heurico 1.16 in 7.15 seconds.