The generator matrix

 1  0  1  1  1 14  0  1  1  1  1  2  4  6  1  1  1  1  1  1  1  1 12  1  1  1  8  1  6  2  1
 0  1 11  6 13  1  1  8  3 14  5  1  1  1  4 10  7 12  9  8  5  1  1  6  9  9  1 13  1  0  0
 0  0 12  0  4  4 12  4  0  4  8  4  4  0  4  8  4  8  0  4  0 12  0  8  8  8 12 12  8  8  0
 0  0  0  8  0  0  0  0  0  0  8  0  8  8  8  0  0  8  0  8  0  8  8  8  8  8  8  0  8  0  0
 0  0  0  0  8  0  0  0  8  8  8  8  8  0  8  0  8  0  8  0  8  0  0  8  8  0  8  0  8  8  0
 0  0  0  0  0  8  0  8  0  8  0  0  0  8  0  8  8  8  0  8  8  8  0  8  0  0  8  8  8  8  0
 0  0  0  0  0  0  8  8  0  8  0  8  8  8  0  8  0  0  8  0  8  8  8  8  8  8  8  8  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+41x^24+52x^25+203x^26+318x^27+1021x^28+1612x^29+3636x^30+2702x^31+3579x^32+1612x^33+986x^34+298x^35+200x^36+52x^37+36x^38+10x^39+19x^40+3x^42+3x^44

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 1.23 seconds.