The generator matrix

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

generates a code of length 14 over Z2[X]/(X^3) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+82x^11+128x^12+242x^13+152x^14+236x^15+75x^16+76x^17+24x^18+2x^19+4x^20+2x^21

The gray image is a linear code over GF(2) with n=56, k=10 and d=22.
This code was found by Heurico 1.11 in 3.62e-008 seconds.