The generator matrix

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

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+248x^9+790x^10+1864x^11+4021x^12+5666x^13+7321x^14+6104x^15+3981x^16+1780x^17+720x^18+208x^19+61x^20+2x^21+1x^22

The gray image is a linear code over GF(2) with n=56, k=15 and d=18.
This code was found by Heurico 1.16 in 3.92 seconds.