The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  1  1  1  4  1  4  1  4  2  2  4  1  1  2  1
 0 12  0  4  0  0  4 12  0  8  4  4  0  8 12  4  8 12  8  8  4  4  8 12  4 12  0  0  4  4  0
 0  0 12  4  0 12  4  0  0  4  0 12  8  4  0  4  4  8  0  4  4  4  0  8  4  0 12  0 12  4  0
 0  0  0  8  0  0  0  0  0  8  8  8  8  0  8  0  8  8  0  8  0  0  0  8  8  8  0  0  0  0  8
 0  0  0  0  8  0  0  0  0  0  0  0  8  8  8  8  8  0  0  0  8  8  8  0  0  8  0  0  0  8  8
 0  0  0  0  0  8  0  0  0  8  0  0  0  0  0  8  8  8  8  0  8  8  8  8  8  0  8  8  8  8  0
 0  0  0  0  0  0  8  0  0  8  8  0  8  0  8  8  0  8  0  8  8  0  8  0  0  0  0  8  0  0  0
 0  0  0  0  0  0  0  8  0  0  8  0  0  0  0  8  0  8  8  8  0  8  0  8  0  8  8  0  0  8  0
 0  0  0  0  0  0  0  0  8  0  0  8  0  8  8  8  0  8  8  0  8  8  0  0  0  0  8  8  0  0  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+30x^23+152x^24+120x^25+310x^26+380x^27+1103x^28+1412x^29+2452x^30+4296x^31+2512x^32+1428x^33+1172x^34+388x^35+270x^36+108x^37+94x^38+26x^39+54x^40+4x^41+22x^42+3x^44+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 2.35 seconds.