The generator matrix

 1  1  1  1  2  2  2  1  1  1
 0  2  0  2  4  2  6 14  2 14
 0  0  2  2  2  2  0  2  6  6
 0  0  0  4  0  0  8  8  4 12
 0  0  0  0  8  0  0  8  0  8
 0  0  0  0  0  8  0  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+148x^6+296x^7+1246x^8+3264x^9+6408x^10+3344x^11+1296x^12+256x^13+100x^14+8x^15+17x^16

The gray image is a code over GF(2) with n=80, k=14 and d=24.
This code was found by Heurico 1.16 in 68.9 seconds.