The generator matrix

 1  1  1  1  2  0  1  1  1  1
 0  2  0  6  2  2  8  6  0  6
 0  0 12  0  0  0  4  8  4  4
 0  0  0 12  0  4  4 12  8  8
 0  0  0  0  4 12  4 12  4 12

generates a code of length 10 over Z16 who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+102x^6+64x^7+528x^8+1728x^9+3340x^10+1728x^11+548x^12+64x^13+78x^14+11x^16

The gray image is a code over GF(2) with n=80, k=13 and d=24.
This code was found by Heurico 1.16 in 0.0963 seconds.