The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  2  1 12  1  2  1  4  1  1  4  1  4  2
 0  2  0  2  8  0  6 14  0  8  6  2  0 10  0  2  4  2 14 12  2 12 12  2 12 12  8  2  0  2  2
 0  0  2  2  0 14  6  8  4 10  2  8  4 14 14 12  2  4  6 10  8 12 10  6  2 10 14 10 10 10  6
 0  0  0  4  4  4  0  4 12  4  8  4  0  4  8 12 12  0  4 12  8  4  0  8  8  4  0  0  8  8 12

generates a code of length 31 over Z16 who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+206x^27+289x^28+502x^29+635x^30+904x^31+624x^32+520x^33+172x^34+134x^35+59x^36+30x^37+8x^38+4x^39+3x^40+4x^41+1x^46

The gray image is a code over GF(2) with n=248, k=12 and d=108.
This code was found by Heurico 1.16 in 21.8 seconds.