The generator matrix
1 1 X X 1
0 X X 0 0
0 0 2 2X+2 0
0 0 0 2X 0
generates a code of length 5 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 2.
Homogenous weight enumerator: w(x)=1x^0+23x^2+44x^3+168x^4+552x^5+168x^6+44x^7+23x^8+1x^10
The gray image is a code over GF(2) with n=40, k=10 and d=8.
This code was found by Heurico 1.16 in 0 seconds.