The generator matrix
1 0 1 X 1
0 1 1 2X+2 0
0 0 X X 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+55x^2+212x^3+680x^4+2200x^5+680x^6+212x^7+55x^8+1x^10
The gray image is a code over GF(2) with n=40, k=12 and d=8.
This code was found by Heurico 1.16 in 0.016 seconds.