The generator matrix

 1  0  0  1  1
 0  1  0  2  5
 0  0  1  1  3

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

Homogenous weight enumerator: w(x)=1x^0+128x^3+738x^4+2368x^5+728x^6+128x^7+5x^8

The gray image is a code over GF(2) with n=40, k=12 and d=12.
This code was found by Heurico 1.16 in -4.77e-008 seconds.