The generator matrix

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

generates a code of length 11 over Z2[X]/(X^3) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+45x^8+98x^9+19x^10+192x^11+18x^12+92x^13+42x^14+2x^17+3x^18

The gray image is a linear code over GF(2) with n=44, k=9 and d=16.
This code was found by Heurico 1.16 in 0.00199 seconds.