The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+87x^6+176x^7+938x^8+1360x^9+3067x^10+1360x^11+944x^12+176x^13+77x^14+5x^16+1x^18

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 0.213 seconds.