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

generates a code of length 31 over Z16 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+111x^28+768x^31+95x^32+48x^36+1x^60

The gray image is a code over GF(2) with n=248, k=10 and d=112.
This code was found by Heurico 1.16 in 44.8 seconds.