The generator matrix
1 1 1 1 1 1 X X 1 1 1
0 X 0 0 0 X X^2 0 X X X^2
0 0 X 0 0 X 0 X X X^2 X
0 0 0 X 0 X X^2 X^2+X X^2 X^2+X X^2+X
0 0 0 0 X X X^2+X X^2 X^2 X X^2+X
0 0 0 0 0 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 6.
Homogenous weight enumerator: w(x)=1x^0+54x^6+104x^7+139x^8+360x^9+840x^10+1104x^11+807x^12+400x^13+158x^14+72x^15+44x^16+8x^17+4x^18+1x^20
The gray image is a linear code over GF(2) with n=44, k=12 and d=12.
This code was found by Heurico 1.16 in 0.0276 seconds.