The generator matrix

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

generates a code of length 11 over Z2[X]/(X^3) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+28x^4+78x^8+128x^10+512x^11+212x^12+57x^16+8x^20

The gray image is a linear code over GF(2) with n=44, k=10 and d=8.
This code was found by Heurico 1.16 in 0.00161 seconds.