The generator matrix
1 0 0 0 0 1 1 1 1 1
0 1 0 0 0 1 0 2 X 0
0 0 1 0 0 1 0 X+2 X+2 0
0 0 0 1 0 1 1 X+1 0 0
0 0 0 0 1 1 X+1 1 X 0
0 0 0 0 0 X X+2 2 0 2
generates a code of length 10 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+107x^4+296x^5+1756x^6+4744x^7+14004x^8+25680x^9+37896x^10+25680x^11+14004x^12+4744x^13+1756x^14+296x^15+107x^16+1x^20
The gray image is a code over GF(2) with n=40, k=17 and d=8.
This code was found by Heurico 1.13 in 0.422 seconds.