The generator matrix

 1  0  1  1  1 14  1  1  6  1  8  1  4 10  1  1  1  1 12  1  1  2  1 14  1  2  1  1  2  2  1
 0  1 11 14  5  1  0  3  1  6  1 13  1  1  4  7 10  9  1 15 12  1  5  1  6 14  0  5 14  8  0
 0  0 12  4  0  4 12  0  0  8 12 12  4  0  4  4  0  8  0  8  0 12  8 12  0  4  8  0  4  4  0
 0  0  0  8  0  0  0  0  0  0  0  8  8  8  0  8  8  8  0  0  8  8  0  8  0  0  0  0  8  8  8
 0  0  0  0  8  0  0  0  0  8  8  0  0  8  0  8  8  0  0  8  0  8  0  8  0  0  8  8  8  8  8
 0  0  0  0  0  8  0  0  0  0  8  0  8  0  8  8  0  0  8  8  8  0  8  8  0  8  8  0  0  0  0
 0  0  0  0  0  0  8  0  0  0  0  8  8  8  8  0  0  8  8  8  8  0  8  0  8  0  0  8  8  0  0
 0  0  0  0  0  0  0  8  0  8  8  0  0  8  8  8  0  8  0  0  8  8  8  8  0  8  0  8  8  0  0
 0  0  0  0  0  0  0  0  8  0  0  0  0  0  0  0  8  8  8  8  8  8  0  8  0  8  0  8  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+46x^22+22x^23+177x^24+228x^25+743x^26+1156x^27+3797x^28+8580x^29+10592x^30+14880x^31+10601x^32+8460x^33+3808x^34+1308x^35+742x^36+140x^37+162x^38+42x^39+37x^40+8x^42+5x^44+1x^58

The gray image is a code over GF(2) with n=248, k=16 and d=88.
This code was found by Heurico 1.16 in 15.6 seconds.