The generator matrix
1 0 1 1 1 X^2 1 1 X 1 1
0 1 1 0 X+1 1 0 X+1 1 X^2+X+1 X+1
0 0 X 0 X X^2 X X^2 0 0 X
0 0 0 X X X^2+X X^2+X X^2 X^2+X X^2+X 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+66x^8+96x^9+264x^10+192x^11+240x^12+96x^13+56x^14+13x^16
The gray image is a linear code over GF(2) with n=44, k=10 and d=16.
This code was found by Heurico 1.16 in 0.00472 seconds.