The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  2  4  1  1  1  2  1  2  1  2  1  4  2  1
 0 12  0  4  0  0  4 12  8 12  0 12  0 12  4  8 12  4  4  8  0  4  8  0  0 12  0 12 12  4  0
 0  0 12  4  0 12  4  8  4  4  0  0  0  4  4  4  8 12 12  4  0  4  4  0 12  8 12 12  0 12  0
 0  0  0  8  0  0  0  0  0  8  8  0  8  0  8  8  8  0  8  0  0  0  8  8  8  0  0  0  8  0  0
 0  0  0  0  8  0  0  8  8  8  8  0  0  8  0  8  8  0  0  8  8  8  0  0  8  8  0  0  8  0  0
 0  0  0  0  0  8  0  0  8  0  8  8  0  8  8  0  0  0  0  8  8  0  8  8  8  0  8  8  8  0  0
 0  0  0  0  0  0  8  0  0  0  8  0  8  8  0  8  8  8  8  8  8  0  8  0  0  8  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+41x^24+34x^25+70x^26+94x^27+165x^28+362x^29+767x^30+1086x^31+745x^32+342x^33+138x^34+90x^35+66x^36+30x^37+40x^38+10x^39+5x^40+8x^42+1x^44+1x^46

The gray image is a code over GF(2) with n=248, k=12 and d=96.
This code was found by Heurico 1.16 in 0.178 seconds.