The generator matrix

 1  0  0  1  1  1  1  4  1  1
 0  1  0  1  2  7 12  1  7  4
 0  0  1  1  1  2  0  3  5  3
 0  0  0  2  0  8  6  2  4 10
 0  0  0  0  8  0  0  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+116x^6+864x^7+4027x^8+15128x^9+25245x^10+15160x^11+4034x^12+840x^13+110x^14+8x^15+2x^16+1x^18

The gray image is a code over GF(2) with n=80, k=16 and d=24.
This code was found by Heurico 1.16 in 1.42 seconds.