The generator matrix
1 1 1 1 1 1 1 X X 1 1
0 X 0 0 0 X X^2+X X^2 0 X 0
0 0 X 0 X X X X^2+X X^2 X^2+X 0
0 0 0 X X 0 X X X X 0
0 0 0 0 X^2 0 0 X^2 X^2 0 0
0 0 0 0 0 X^2 0 0 X^2 X^2 X^2
generates a code of length 11 over Z2[X]/(X^3) who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+24x^6+42x^7+87x^8+186x^9+402x^10+564x^11+399x^12+196x^13+84x^14+34x^15+24x^16+2x^17+2x^18+1x^20
The gray image is a linear code over GF(2) with n=44, k=11 and d=12.
This code was found by Heurico 1.16 in 0.00816 seconds.