The generator matrix

 1  0  0  0  0  1  1  1 X^2  1  0  X  1  X
 0  1  0  0  0 X^2  1 X^2+1  1 X^2  X  1  1  1
 0  0  1  0  0 X^2+X+1 X+1  X X^2+X+1  X  1  1 X^2+X+1  0
 0  0  0  1  0  1  X X^2+1 X^2+X+1 X+1  X  X X^2  0
 0  0  0  0  1  1 X^2  X  X X^2+X+1 X^2+1 X^2+X X^2+1  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+238x^9+856x^10+1766x^11+4068x^12+5576x^13+7530x^14+5868x^15+4171x^16+1694x^17+732x^18+206x^19+48x^20+12x^21+2x^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 1.13 in 1.26 seconds.