The generator matrix

 1  1  1  1  2  2  2  1  1  2
 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  0  8
 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

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

Homogenous weight enumerator: w(x)=1x^0+69x^4+272x^6+1850x^8+12000x^10+1850x^12+272x^14+69x^16+1x^20

The gray image is a code over GF(2) with n=80, k=14 and d=16.
This code was found by Heurico 1.16 in 0.111 seconds.