The generator matrix
1 1 1 1 X 1 1 1 1 1 1
0 X 0 0 X 0 X X+2 2 0 0
0 0 X 0 X X X X+2 X 0 0
0 0 0 X X X 0 X+2 0 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 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+68x^4+264x^6+710x^8+2008x^10+2048x^11+2092x^12+632x^14+321x^16+40x^18+8x^20
The gray image is a code over GF(2) with n=44, k=13 and d=8.
This code was found by Heurico 1.16 in 0.0614 seconds.