The generator matrix
1 1 1 1 X X 1 1 1 1 1
0 X 0 X+2 X X 0 0 0 0 0
0 0 2 0 0 0 0 0 0 2 0
0 0 0 2 0 0 0 0 0 2 0
0 0 0 0 2 0 0 0 0 2 0
0 0 0 0 0 2 0 0 0 2 0
0 0 0 0 0 0 2 0 0 2 0
0 0 0 0 0 0 0 2 0 2 0
0 0 0 0 0 0 0 0 2 2 0
generates a code of length 11 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+44x^4+49x^6+214x^8+512x^9+204x^10+2048x^11+204x^12+512x^13+214x^14+49x^16+44x^18+1x^22
The gray image is a code over GF(2) with n=44, k=12 and d=8.
This code was found by Heurico 1.16 in 0.0174 seconds.