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.