The generator matrix

 1  0  1  1  1  6  1  1  8  1  1 14  1  4  1  1  6  1  8  1  1  4  1  6  1  0  1  2 12  2  1
 0  1 11  6  1  1  8 11  1 13  6  1 10  1  3  8  1 14  1 11  2  1  0  1 15  1  9  4  1  8  8
 0  0 12  0  0  0  0  0  8  4  4  4  4  8  0 12  0  8 12  8  4  8  8 12  4  4  0  0  4 12  0
 0  0  0 12  0  0 12  8 12  0  0 12  0  4  8  8  4  0  0 12  4  8 12  8 12 12 12  0  4  8  0
 0  0  0  0  4  0  8  4  0  8  4 12 12  0  8  8 12 12  8  0 12  4 12  4  0  0  4  4  0  0  4
 0  0  0  0  0  8  8  8  0  8  8  8  0  8  8  0  8  0  0  0  0  0  8  0  0  8  8  8  8  8  8

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

Homogenous weight enumerator: w(x)=1x^0+57x^24+164x^25+317x^26+850x^27+1653x^28+3678x^29+6206x^30+6988x^31+6119x^32+3742x^33+1658x^34+804x^35+286x^36+122x^37+70x^38+28x^39+11x^40+6x^41+5x^42+2x^43+1x^44

The gray image is a code over GF(2) with n=248, k=15 and d=96.
This code was found by Heurico 1.16 in 5.06 seconds.