The generator matrix

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

generates a code of length 11 over Z2[X]/(X^3) who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+40x^7+79x^8+224x^9+432x^10+496x^11+439x^12+224x^13+64x^14+40x^15+8x^16+1x^20

The gray image is a linear code over GF(2) with n=44, k=11 and d=14.
This code was found by Heurico 1.16 in 0.0116 seconds.