The generator matrix

 1  0  0  1  1  1 X^2  1  1  1 X^2  1 X^2+X X^2+X
 0  1  0  1  X X^2+X+1  1  0 X^2 X^2+1  1  1  X  1
 0  0  1  1  1  0 X+1  X X+1  0  X  1  1  1
 0  0  0  X  0 X^2+X  X X^2+X X^2+X  0 X^2 X^2 X^2+X X^2+X
 0  0  0  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0
 0  0  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2 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+48x^9+212x^10+368x^11+1279x^12+1120x^13+2136x^14+1120x^15+1279x^16+368x^17+212x^18+48x^19+1x^28

The gray image is a linear code over GF(2) with n=56, k=13 and d=18.
This code was found by Heurico 1.16 in 0.272 seconds.