The generator matrix

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

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+34x^8+24x^10+128x^11+48x^12+8x^14+13x^16

The gray image is a linear code over GF(2) with n=44, k=8 and d=16.
This code was found by Heurico 1.16 in 0.000752 seconds.