The generator matrix

 1  1  1  2  1
 0  2  0  6 14
 0  0 12  8  4

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

Homogenous weight enumerator: w(x)=1x^0+16x^3+98x^4+288x^5+88x^6+16x^7+5x^8

The gray image is a code over GF(2) with n=40, k=9 and d=12.
This code was found by Heurico 1.16 in 0.000247 seconds.