The generator matrix

 1  1  1  1  X  X  1  1  1  1  1
 0  X  0 X^2+X  X  X  0  0  0  0  0
 0  0 X^2  0  0  0  0  0  0 X^2  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+44x^4+49x^6+214x^8+512x^9+204x^10+2048x^11+204x^12+512x^13+214x^14+49x^16+44x^18+1x^22

The gray image is a linear code over GF(2) with n=44, k=12 and d=8.
This code was found by Heurico 1.16 in 0.0154 seconds.