The generator matrix

 1  1  1  1  2
 0  2  0  0  6
 0  0  2  0  2
 0  0  0  2  2
 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+125x^2+480x^3+3074x^4+9024x^5+3074x^6+480x^7+125x^8+1x^10

The gray image is a code over GF(2) with n=40, k=14 and d=8.
This code was found by Heurico 1.16 in 0.0263 seconds.