The generator matrix

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

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+63x^4+32x^5+56x^6+192x^7+754x^8+1504x^9+3096x^10+4736x^11+3558x^12+1504x^13+424x^14+192x^15+221x^16+32x^17+8x^18+11x^20

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 0.179 seconds.