The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+226x^27+214x^28+622x^29+572x^30+944x^31+569x^32+532x^33+125x^34+180x^35+47x^36+46x^37+6x^38+8x^39+1x^42+2x^43+1x^44

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 24.5 seconds.