The generator matrix

 1  0  1  1  1 14  2  2  1  1
 0  1 11  6  5  1  6 14  8  0
 0  0 12  0  4  8  4  4  8  0
 0  0  0 12  4 12 12  8 12  0

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

Homogenous weight enumerator: w(x)=1x^0+16x^6+144x^7+231x^8+1008x^9+1296x^10+1008x^11+231x^12+144x^13+16x^14+1x^20

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 0.0105 seconds.