The generator matrix

 1  0  1  1  1 14  1  1  0  1 14  1  1  6  1  1  1  8 10 12  1  1  2  1  1  1  1 14  2  0  1
 0  1 11  6  5  1 11  0  1  5  1 14 13  1  8  3  4  1  1  2  6 10 14  9  3 13  5  1 14  1  0
 0  0 12  0  0  0  0  4  4 12 12  4  8  4  4  4  8 12  0  4 12  8  0  0  4 12  8 12 12  0  0
 0  0  0 12  0  4  4  4 12 12  8  0  4  4  0  4  4  8  8  4 12  0  4  0  4  8  0  0  8  8  0
 0  0  0  0  8  0  0  0  0  0  8  0  8  0  8  8  0  8  0  8  0  0  8  8  0  8  0  0  8  8  0
 0  0  0  0  0  8  0  0  0  8  0  0  8  8  8  8  8  0  8  8  0  8  8  8  0  0  8  0  0  8  0
 0  0  0  0  0  0  8  0  8  0  0  8  0  8  0  0  8  0  8  8  8  8  0  0  8  8  0  8  0  8  0
 0  0  0  0  0  0  0  8  0  0  0  8  0  8  8  0  0  8  8  0  0  8  8  0  8  8  8  0  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+21x^22+68x^23+204x^24+248x^25+707x^26+1890x^27+3263x^28+7934x^29+12197x^30+12478x^31+12185x^32+7942x^33+3276x^34+1906x^35+700x^36+250x^37+165x^38+38x^39+26x^40+10x^41+17x^42+4x^43+5x^44+1x^46

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 16.3 seconds.