The generator matrix

 1  0  1  1  1 X^2+X  1  1  1  1  1
 0  1 X+1 X^2+X X^2+1  1  0 X^2+X X^2+X  X  0
 0  0 X^2  0 X^2  0  0 X^2  0 X^2  0
 0  0  0 X^2 X^2 X^2 X^2 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+13x^8+24x^9+83x^10+16x^11+82x^12+24x^13+10x^14+3x^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 0.000708 seconds.