The generator matrix

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

generates a code of length 28 over Z16 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+68x^20+116x^22+323x^24+128x^25+832x^26+1408x^27+2449x^28+1408x^29+840x^30+128x^31+293x^32+128x^34+58x^36+4x^38+7x^40+1x^44

The gray image is a code over GF(2) with n=224, k=13 and d=80.
This code was found by Heurico 1.16 in 0.481 seconds.