The generator matrix

 1  1  1  1  1  1  1  1  2  1  0  1  2  1  2  1  1  1  1  1 12  0  2  1  1  2  1  1
 0  2 12  6  0  6 12 10  6  0  2 10 10 12  6  6  0 12  6 10  2  2  6  0  6  0  0  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  8  0  0  8  8  0  0  8  8  8  8  8  8  8  8
 0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  0  0  8  8  8  8  8  8  8  8  0  0
 0  0  0  0  8  0  0  0  0  8  0  0  8  8  8  8  8  0  8  0  0  0  0  8  0  0  8  0
 0  0  0  0  0  8  0  0  0  0  0  8  8  0  8  0  8  8  8  8  0  0  0  8  8  8  0  8
 0  0  0  0  0  0  8  0  0  8  8  0  0  0  8  8  8  8  0  8  0  0  8  0  8  8  0  8
 0  0  0  0  0  0  0  8  0  0  8  8  0  8  8  8  0  8  8  0  0  8  8  0  0  0  8  8
 0  0  0  0  0  0  0  0  8  0  8  0  8  0  8  0  0  0  0  0  8  8  8  8  8  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+71x^20+108x^22+64x^23+590x^24+704x^25+1548x^26+3840x^27+2538x^28+3840x^29+1572x^30+704x^31+552x^32+64x^33+100x^34+79x^36+8x^40+1x^48

The gray image is a code over GF(2) with n=224, k=14 and d=80.
This code was found by Heurico 1.16 in 1.51 seconds.