The generator matrix

 1  0  0  1  1  1  X  1  1  X  1
 0  1  0  X X^2+1 X^2+X+1  1 X^2+X X^2  0  0
 0  0  1  1 X+1  X X^2+1 X^2+X+1  1 X^2+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+33x^8+100x^9+32x^10+196x^11+30x^12+76x^13+24x^14+12x^15+8x^16

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 0.0013 seconds.