The generator matrix

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

generates a code of length 14 over Z2[X]/(X^3) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+36x^10+132x^11+308x^12+318x^13+474x^14+324x^15+283x^16+112x^17+48x^18+8x^19+2x^21+2x^22

The gray image is a linear code over GF(2) with n=56, k=11 and d=20.
This code was found by Heurico 1.16 in 0.02 seconds.