The generator matrix

 1  1  1  1  2  0  1  1  1  1
 0  2  0 14  6  2  4  0  8  4
 0  0 12  4  0 12  4  0 12  4
 0  0  0  8  0  0  8  8  0  0
 0  0  0  0  8  0  8  8  0  8
 0  0  0  0  0  8  8  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+58x^6+316x^8+768x^9+1812x^10+768x^11+316x^12+50x^14+7x^16

The gray image is a code over GF(2) with n=80, k=12 and d=24.
This code was found by Heurico 1.16 in 0.0134 seconds.