The generator matrix
1 0 0 0 1
0 1 0 0 2X
0 0 1 0 0
0 0 0 1 0
0 0 0 0 2
generates a code of length 5 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 1.
Homogenous weight enumerator: w(x)=1x^0+46x^1+813x^2+7464x^3+43986x^4+157524x^5+43986x^6+7464x^7+813x^8+46x^9+1x^10
The gray image is a code over GF(2) with n=40, k=18 and d=4.
This code was found by Heurico 1.16 in 4.12 seconds.