The generator matrix
1 0 1 1 1
0 1 0 0 2
0 0 X 0 0
0 0 0 X 0
0 0 0 0 X
generates a code of length 5 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 1.
Homogenous weight enumerator: w(x)=1x^0+14x^1+77x^2+232x^3+690x^4+2068x^5+690x^6+232x^7+77x^8+14x^9+1x^10
The gray image is a code over GF(2) with n=20, k=12 and d=2.
This code was found by Heurico 1.16 in 0.00235 seconds.