The generator matrix

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

generates a code of length 5 over Z16 who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+8x^3+34x^4+176x^5+24x^6+8x^7+5x^8

The gray image is a code over GF(2) with n=40, k=8 and d=12.
This code was found by Heurico 1.16 in 0.000137 seconds.