The generator matrix

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

generates a code of length 28 over Z16 who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+72x^22+548x^23+1446x^24+3416x^25+8072x^26+11110x^27+16132x^28+11220x^29+8168x^30+3402x^31+1311x^32+464x^33+104x^34+42x^35+20x^36+4x^37+2x^39+2x^40

The gray image is a code over GF(2) with n=224, k=16 and d=88.
This code was found by Heurico 1.16 in 12.7 seconds.