The generator matrix

 1  0  0  1  1  1  2  1  1  1  1  4  0  6 14 12  1  1  4  1  1  1  6 12  8  1  1 10  1  1  1
 0  1  0  2  5  7  1  0 14  9  7  1  1  6  4  1 10  2  2  1  6  7  1  1  1  7 10  0  7  3  0
 0  0  1  1  3  2  1  6  7  5  4  2  3  1  1  5  6  7  1  7  0  1  6  3  4  2  6  1  4  3  0
 0  0  0  8  0  0  0  0  8  8  8  0  0  8  8  0  0  0  8  8  8  8  0  8  8  8  0  0  8  0  0
 0  0  0  0  8  0  0  0  0  8  0  8  8  8  0  8  8  0  0  0  8  0  8  0  0  8  8  0  8  8  0
 0  0  0  0  0  8  0  0  0  0  8  8  8  8  0  0  0  0  8  0  0  8  8  8  0  0  8  8  8  0  0
 0  0  0  0  0  0  8  8  8  0  0  0  8  8  0  0  0  8  8  0  8  8  8  0  0  8  0  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+26x^24+170x^25+578x^26+1688x^27+3972x^28+7290x^29+11556x^30+15038x^31+11573x^32+7230x^33+3956x^34+1678x^35+538x^36+158x^37+36x^38+26x^39+16x^40+2x^42+2x^43+2x^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 13.4 seconds.