The generator matrix

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

generates a code of length 14 over Z2[X]/(X^3) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+36x^9+63x^10+120x^11+260x^12+348x^13+389x^14+368x^15+243x^16+124x^17+57x^18+24x^19+8x^20+4x^21+3x^22

The gray image is a linear code over GF(2) with n=56, k=11 and d=18.
This code was found by Heurico 1.16 in 0.0241 seconds.