The generator matrix

 1  1  1  1  1  1  1  1  X  X  1
 0  X  0  X  0 X^2  X X^2+X X^2  0  0
 0  0  X  X  0  X X^2+X X^2  X X^2+X  0
 0  0  0 X^2 X^2 X^2  0 X^2  0  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+21x^8+48x^9+9x^10+96x^11+10x^12+48x^13+22x^14+1x^18

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 0.000867 seconds.