The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  2  2  4  2  1  1  1  1
 0 12  0  0  0  0  0  0  0  0  4  8 12 12  8  4  8  4  4  0  4 12  0  4  8 12  4  4 12 12 12
 0  0 12  0  0  0  4 12 12  8  4  0 12  8 12  4  4  4  8  4 12  4  8  8  4  8  0  4  0  4 12
 0  0  0 12  0  4  4  4  0  8  0  0  0  0  8  4  0 12 12  4  8 12  0 12  8  4  8  4  8  4  4
 0  0  0  0 12  4  8  4  4  0  8  4 12  4 12 12  0 12  0  0  0  8  4  0  8  4  4  4  4 12  4
 0  0  0  0  0  8  8  0  8  8  0  8  8  8  8  0  8  8  8  0  8  8  0  0  0  0  0  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+68x^24+114x^25+109x^26+200x^27+284x^28+412x^29+1612x^30+2632x^31+1560x^32+472x^33+274x^34+152x^35+116x^36+84x^37+52x^38+24x^39+18x^40+6x^41+1x^42+1x^48

The gray image is a code over GF(2) with n=248, k=13 and d=96.
This code was found by Heurico 1.16 in 0.643 seconds.