The generator matrix

 1  0  0  1  1  1  1  6  1  1
 0  1  0  1  6 15  4  1  5  0
 0  0  1  1 11  2  2  3  3  0
 0  0  0 12  0  8  4 12  0  0
 0  0  0  0 12 12  4  4  8  0

generates a code of length 10 over Z16 who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+44x^5+251x^6+1310x^7+4798x^8+12978x^9+26755x^10+12988x^11+4824x^12+1312x^13+225x^14+38x^15+9x^16+2x^17+1x^18

The gray image is a code over GF(2) with n=80, k=16 and d=20.
This code was found by Heurico 1.16 in 0.83 seconds.