The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+67x^22+120x^23+214x^24+310x^25+443x^26+496x^27+601x^28+1228x^29+6832x^30+12048x^31+6871x^32+1272x^33+698x^34+528x^35+390x^36+244x^37+197x^38+120x^39+50x^40+18x^41+18x^42+1x^44+1x^58

The gray image is a code over GF(2) with n=248, k=15 and d=88.
This code was found by Heurico 1.16 in 9.12 seconds.