The generator matrix
1 1 X 1 1
0 2 2 0 0
0 0 2X 0 0
0 0 0 2X 0
generates a code of length 5 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 2.
Homogenous weight enumerator: w(x)=1x^0+7x^2+40x^4+160x^5+40x^6+7x^8+1x^10
The gray image is a code over GF(2) with n=40, k=8 and d=8.
This code was found by Heurico 1.16 in 0 seconds.