The generator matrix

 1  1  X  1  1  1  1  1  1  1  1
 0  X  X  0  0  0  0  0  0  0  0
 0  0 X^2  0  0  0  0  0  0  0  0
 0  0  0 X^2  0  0  0  0  0  0  0
 0  0  0  0 X^2  0  0  0  0  0  0
 0  0  0  0  0 X^2  0  0  0  0  0
 0  0  0  0  0  0 X^2  0  0  0  0
 0  0  0  0  0  0  0 X^2  0  0  0
 0  0  0  0  0  0  0  0 X^2  0  0
 0  0  0  0  0  0  0  0  0 X^2  0
 0  0  0  0  0  0  0  0  0  0 X^2

generates a code of length 11 over Z2[X]/(X^3) who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+15x^2+91x^4+309x^6+666x^8+5062x^10+4096x^11+5062x^12+666x^14+309x^16+91x^18+15x^20+1x^22

The gray image is a linear code over GF(2) with n=44, k=14 and d=4.
This code was found by Heurico 1.16 in 0.122 seconds.