The generator matrix
1 1 1 1 1
0 2 0 2X+2 0
0 0 2 2X+2 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+15x^2+12x^3+16x^4+424x^5+16x^6+12x^7+15x^8+1x^10
The gray image is a code over GF(2) with n=40, k=9 and d=8.
This code was found by Heurico 1.16 in -1.01e-007 seconds.