The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  1
 0  1 X+1 X^2+X  1  1  0 X+1  1  0  0
 0  0 X^2  0  0  0  0 X^2  0  0 X^2
 0  0  0 X^2  0  0  0 X^2  0 X^2 X^2
 0  0  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
 0  0  0  0  0  0 X^2 X^2  0 X^2  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+16x^6+16x^7+78x^8+192x^9+548x^10+352x^11+544x^12+192x^13+72x^14+16x^15+17x^16+4x^18

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 0.00508 seconds.