The generator matrix
1 0 1 X 1
0 1 1 0 0
0 0 X X 0
0 0 0 2 0
0 0 0 0 2
generates a code of length 5 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 2.
Homogenous weight enumerator: w(x)=1x^0+25x^2+72x^3+230x^4+368x^5+230x^6+72x^7+25x^8+1x^10
The gray image is a code over GF(2) with n=20, k=10 and d=4.
This code was found by Heurico 1.16 in 0.000357 seconds.