The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  2  8  8  2  1  1  1  1 12  0  1  2  0  1  1  1
 0  2  0  6  4  6 12  2  8 14  4 10 12  6  2 14  2  2  2  0  6  6  4  2  0  6 10  2  2  2  2
 0  0 12  0  4  0  0  0  8  4  8  4 12  4  0  4  8 12 12 12  8  0 12  4  4 12 12  8 12  0  0
 0  0  0 12  0  0  0  4 12  8  4  4  4  4  0  8  4  0  8  4  8  8 12 12  0 12  4  8  0 12  4
 0  0  0  0  8  0  0  0  0  8  0  8  8  0  8  0  8  0  0  0  8  8  8  8  0  8  8  0  8  8  0
 0  0  0  0  0  8  0  0  0  0  8  8  8  8  0  0  0  8  8  0  8  8  0  8  0  8  0  0  8  0  8
 0  0  0  0  0  0  8  8  0  8  0  8  0  0  0  8  8  8  0  8  8  0  0  8  8  0  8  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+61x^24+130x^25+306x^26+428x^27+1135x^28+1916x^29+2550x^30+3248x^31+2732x^32+1940x^33+1045x^34+396x^35+269x^36+108x^37+61x^38+24x^39+26x^40+2x^41+5x^42+1x^46

The gray image is a code over GF(2) with n=248, k=14 and d=96.
This code was found by Heurico 1.16 in 2.09 seconds.