The generator matrix

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

generates a code of length 10 over Z16 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+52x^4+104x^6+128x^7+622x^8+384x^9+5624x^10+384x^11+580x^12+128x^13+152x^14+25x^16+8x^18

The gray image is a code over GF(2) with n=80, k=13 and d=16.
This code was found by Heurico 1.16 in 0.0265 seconds.