The generator matrix

 1  1  1  1  1  1  1  1  X  1  X
 0  X  0  0  0  X X^2+X  X X^2+X  0 X^2
 0  0  X  0  X  X  X X^2  X  0 X^2+X
 0  0  0  X  X X^2 X^2+X X^2+X  X  0  X
 0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2

generates a code of length 11 over Z2[X]/(X^3) who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+26x^7+60x^8+90x^9+202x^10+276x^11+188x^12+100x^13+52x^14+18x^15+7x^16+2x^17+2x^18

The gray image is a linear code over GF(2) with n=44, k=10 and d=14.
This code was found by Heurico 1.16 in 0.00474 seconds.