The generator matrix

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

generates a code of length 11 over Z2[X]/(X^3) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+74x^5+373x^6+1880x^7+5660x^8+15370x^9+25683x^10+32928x^11+25764x^12+15390x^13+5643x^14+1864x^15+351x^16+78x^17+13x^18

The gray image is a linear code over GF(2) with n=44, k=17 and d=10.
This code was found by Heurico 1.13 in 1.64 seconds.