The generator matrix
1 1 1 1 1 X 1 1 1 1 1
0 X 0 0 0 0 X X^2+X X 0 0
0 0 X 0 0 X X X^2+X 0 0 0
0 0 0 X 0 X 0 0 0 X^2 0
0 0 0 0 X X 0 X^2+X X X^2 0
0 0 0 0 0 X^2 0 0 X^2 0 0
0 0 0 0 0 0 X^2 0 X^2 0 0
0 0 0 0 0 0 0 X^2 X^2 0 0
generates a code of length 11 over Z2[X]/(X^3) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+70x^4+366x^6+1288x^8+4398x^10+4096x^11+4482x^12+1210x^14+423x^16+42x^18+8x^20
The gray image is a linear code over GF(2) with n=44, k=14 and d=8.
This code was found by Heurico 1.16 in 0.257 seconds.