The generator matrix

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

generates a code of length 11 over Z2[X]/(X^3) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+10x^9+31x^10+48x^11+30x^12+2x^13+1x^14+4x^15+1x^20

The gray image is a linear code over GF(2) with n=44, k=7 and d=18.
This code was found by Heurico 1.16 in 0.00045 seconds.