The generator matrix

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

generates a code of length 31 over Z16 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+42x^24+176x^25+307x^26+558x^27+1071x^28+1814x^29+2729x^30+3094x^31+2580x^32+1838x^33+1148x^34+554x^35+233x^36+130x^37+66x^38+18x^39+9x^40+10x^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 2.18 seconds.