The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+28x^22+40x^23+109x^24+252x^25+343x^26+558x^27+1098x^28+1978x^29+2563x^30+2518x^31+2504x^32+1946x^33+1036x^34+682x^35+346x^36+174x^37+120x^38+42x^39+33x^40+2x^41+5x^42+4x^44+1x^46+1x^48

The gray image is a code over GF(2) with n=248, k=14 and d=88.
This code was found by Heurico 1.16 in 2.34 seconds.