The generator matrix
1 1 1 1 2
0 2 0 0 2
0 0 2 0 2
0 0 0 2 2
generates a code of length 5 over Z4 who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+18x^4+8x^6+5x^8
The gray image is a code over GF(2) with n=10, k=5 and d=4.
This code was found by Heurico 1.16 in 8.3e-005 seconds.