The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  2  0  2  1  1  8  1  1  1  1  2  1  2  1  4  2  2  8  0  2
 0  2  0  6  0 14  0  6  2 12  6 14  2 14  4  8  2 14  4 10  0  6 10  6 12  0 10  8  2  2  4
 0  0 12  0  0  0  4  4  4  8  0  0  4  4  8  8  8 12 12 12  0  4  0  4  0 12  8 12  8  8  0
 0  0  0 12  0  0  0  0  0  0  0  8  8  8  0  4 12  4  4 12  4  4 12  8  0  4  0 12  8 12  8
 0  0  0  0 12  4  4  4  8  0  0 12 12  0 12  8  8  4  4  0 12  8 12  4  8  4  8 12 12  4 12
 0  0  0  0  0  8  0  8  8  0  8  0  0  8  8  0  8  0  0  0  0  0  8  8  8  0  8  8  8  0  8
 0  0  0  0  0  0  8  8  0  8  8  8  8  0  0  8  8  8  0  0  0  0  8  0  0  0  8  8  0  8  0

generates a code of length 31 over Z16 who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+60x^23+164x^24+270x^25+550x^26+1082x^27+2006x^28+3696x^29+5471x^30+6130x^31+5498x^32+3744x^33+2007x^34+1122x^35+501x^36+216x^37+157x^38+50x^39+19x^40+10x^41+7x^42+4x^43+1x^44+2x^48

The gray image is a code over GF(2) with n=248, k=15 and d=92.
This code was found by Heurico 1.16 in 8.34 seconds.