The generator matrix

 1  0  0  1  1  1  X  1  1  X  1
 0  1  0  1  X X+1  1  1 X^2+X+1 X^2+X  0
 0  0  1  X  1 X+1 X+1 X^2  X  0  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+29x^8+104x^9+40x^10+192x^11+22x^12+72x^13+32x^14+16x^15+4x^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 1.11 in -1.01e-007 seconds.