The generator matrix
1 0 0 1 1
0 1 0 1 0
0 0 1 1 0
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+89x^2+504x^3+2278x^4+10640x^5+2278x^6+504x^7+89x^8+1x^10
The gray image is a code over GF(2) with n=40, k=14 and d=8.
This code was found by Heurico 1.16 in 0.031 seconds.