The generator matrix

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

generates a code of length 11 over Z2[X]/(X^3) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+17x^6+77x^8+64x^9+289x^10+128x^11+291x^12+64x^13+75x^14+14x^16+3x^18+1x^20

The gray image is a linear code over GF(2) with n=44, k=10 and d=12.
This code was found by Heurico 1.16 in 0.00257 seconds.