The generator matrix

 1  0  1  1  1 14  1  1  1  1 12  2  8  6  1  1  1  1  1  1  1  2 12  1  2  0  1 10  1  1  1
 0  1 11 14  5  1  8  3  6 13  1  1  1  1 12 15  2 15  1  2 12  0  1 14  6  2  9  1  0 12 10
 0  0 12  4  8 12  4  8  0 12  0  4  4  0  0  8 12  4  4  0 12 12 12  8  4  4  0  8  8  8  0

generates a code of length 31 over Z16 who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+198x^29+318x^30+168x^31+125x^32+108x^33+64x^34+24x^35+14x^37+2x^38+2x^40

The gray image is a code over GF(2) with n=248, k=10 and d=116.
This code was found by Heurico 1.16 in 19.9 seconds.