The generator matrix

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

generates a code of length 31 over Z16 who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+29x^22+12x^23+63x^24+56x^25+154x^26+128x^27+464x^28+712x^29+1851x^30+1256x^31+1851x^32+712x^33+464x^34+128x^35+156x^36+56x^37+55x^38+12x^39+20x^40+6x^42+4x^44+1x^46+1x^56

The gray image is a code over GF(2) with n=248, k=13 and d=88.
This code was found by Heurico 1.16 in 0.621 seconds.