The generator matrix

 1  1  1  1  2
 0 12  0  0 12
 0  0 12  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+45x^2+338x^4+1280x^5+338x^6+45x^8+1x^10

The gray image is a code over GF(2) with n=40, k=11 and d=8.
This code was found by Heurico 1.16 in 0.000828 seconds.