The generator matrix

 1  0  0  0  1
 0  1  0  0  2
 0  0  1  0  0
 0  0  0  1  0
 0  0  0  0 X^2

generates a code of length 5 over Z4[X]/(X^3+2,2X) 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 4.05 seconds.