The generator matrix

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

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+96x^10+262x^11+546x^12+784x^13+768x^14+732x^15+535x^16+256x^17+96x^18+14x^19+6x^20

The gray image is a linear code over GF(2) with n=56, k=12 and d=20.
This code was found by Heurico 1.16 in 0.0721 seconds.