The generator matrix

 1  0  0  1  1
 0  1  0  1  0
 0  0  1  1  0
 0  0  0  2  0

generates a code of length 5 over Z4 who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+15x^2+12x^3+16x^4+40x^5+16x^6+12x^7+15x^8+1x^10

The gray image is a code over GF(2) with n=10, k=7 and d=2.
This code was found by Heurico 1.16 in 7.2e-005 seconds.