The generator matrix

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

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+76x^4+273x^6+128x^7+886x^8+1792x^9+2860x^10+4352x^11+2860x^12+1792x^13+886x^14+128x^15+273x^16+76x^18+1x^22

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 0.172 seconds.