The generator matrix

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

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+124x^7+423x^8+980x^9+1472x^10+2136x^11+1559x^12+1000x^13+368x^14+108x^15+16x^16+4x^17+1x^20

The gray image is a linear code over GF(2) with n=44, k=13 and d=14.
This code was found by Heurico 1.11 in 2.16 seconds.