The generator matrix

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

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+64x^9+192x^10+490x^11+953x^12+1464x^13+1790x^14+1532x^15+989x^16+504x^17+161x^18+42x^19+9x^20+1x^26

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 0.3 seconds.