The generator matrix
1 0 1 1 1 X^2+X 1 1 1 1 X
0 1 X+1 X^2+X 1 1 0 0 X^2+X X^2+X X^2+X
0 0 X^2 0 0 X^2 X^2 X^2 0 0 0
0 0 0 X^2 0 X^2 X^2 0 0 X^2 0
0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 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+44x^8+32x^9+144x^10+64x^11+156x^12+32x^13+32x^14+7x^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 1.16 in 0.00142 seconds.