The generator matrix

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

generates a code of length 5 over Z16 who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+53x^2+48x^3+842x^4+2208x^5+842x^6+48x^7+53x^8+1x^10

The gray image is a code over GF(2) with n=40, k=12 and d=8.
This code was found by Heurico 1.16 in 0.00247 seconds.