The generator matrix

 1  1  1  1  1  1  1  1  1  1  2  1  1  2  1  1  4  2  1  1  1  1  1  1  1  1  1  1
 0 12  0 12  0 12  0 12  8  4 12 12  0 12  0  8 12 12 12 12  0  0  8  8 12  4  0  0
 0  0  8  0  0  0  0  0  8  0  0  0  0  8  8  8  0  8  0  0  0  8  8  0  8  8  0  0
 0  0  0  8  0  0  0  0  0  8  0  8  0  8  8  8  0  0  8  0  8  0  0  0  8  8  0  0
 0  0  0  0  8  0  0  0  0  0  0  0  8  0  8  8  8  8  8  0  8  0  8  0  8  0  0  0
 0  0  0  0  0  8  0  0  0  0  8  8  0  8  0  0  8  8  8  0  8  8  8  8  0  8  0  0
 0  0  0  0  0  0  8  0  8  0  8  8  8  8  8  0  0  8  8  8  8  0  0  0  8  0  0  0
 0  0  0  0  0  0  0  8  0  8  8  8  8  0  8  0  8  0  0  0  8  8  8  0  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+49x^20+44x^22+152x^24+64x^25+148x^26+960x^27+1270x^28+960x^29+148x^30+64x^31+140x^32+44x^34+41x^36+10x^40+1x^48

The gray image is a code over GF(2) with n=224, k=12 and d=80.
This code was found by Heurico 1.16 in 0.142 seconds.