The generator matrix
1 1 X 1 1
0 X X 0 0
0 0 2X+2 0 2X
0 0 0 2 2X
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+25x^2+40x^3+358x^4+1200x^5+358x^6+40x^7+25x^8+1x^10
The gray image is a code over GF(2) with n=40, k=11 and d=8.
This code was found by Heurico 1.16 in 1.05e-007 seconds.