The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1
 0 12  0  0  0  0  0  0  0  0  8 12 12  4  0  0 12 12  4 12  0  4  8  8  8 12 12  8  8  0 12
 0  0 12  0  0  0  0  0  0  0 12 12  4  8  8  4  4  0  8 12 12 12  8  0 12 12  0  0  4  8  8
 0  0  0 12  0  0  8 12 12  4  4  8  4  4  8  0  8 12  4  0  0  8  8  4  4  4  4  0  8  0  4
 0  0  0  0 12  0 12 12  4  8  0  0  0  0  0  8  4 12 12  8  8  0 12  0 12  0  8  8  4  4  4
 0  0  0  0  0 12  4  8  4  4  0  0  0  0  8 12 12  8 12  8  0 12  0  8  0  4  8 12  4  0 12

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

Homogenous weight enumerator: w(x)=1x^0+266x^24+464x^26+609x^28+1700x^30+10240x^31+1785x^32+616x^34+446x^36+228x^38+28x^40+1x^60

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 51.5 seconds.