The generator matrix

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

generates a code of length 10 over Z16 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+68x^4+232x^6+192x^7+1118x^8+2880x^9+7416x^10+2880x^11+1076x^12+192x^13+280x^14+41x^16+8x^18

The gray image is a code over GF(2) with n=80, k=14 and d=16.
This code was found by Heurico 1.16 in 0.063 seconds.