The generator matrix

 1  1  1  1  X  X  X  1  1  1  1
 0  X  0  X  0  X  X  0  0  0  0
 0  0  X  X  X  X  0  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

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+79x^4+168x^6+1346x^8+1536x^9+2376x^10+5120x^11+2838x^12+1536x^13+1016x^14+333x^16+24x^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 0.24 seconds.