The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+54x^27+184x^28+262x^29+464x^30+174x^31+449x^32+218x^33+168x^34+38x^35+9x^36+14x^37+6x^39+4x^40+2x^41+1x^44

The gray image is a code over GF(2) with n=248, k=11 and d=108.
This code was found by Heurico 1.16 in 0.0546 seconds.