The generator matrix

 1  0  0  0  1  1  1  X  1  1  1  0  1  1
 0  1  0  0  1 X^2 X+1  1  X X^2+X  X  1 X+1  0
 0  0  1  0  1 X^2+1 X^2 X+1  0 X+1  X  X X^2+1  X
 0  0  0  1 X^2  1 X^2+1  1 X+1  X  1 X^2+X+1 X^2+X+1 X^2+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+76x^10+304x^11+558x^12+720x^13+786x^14+736x^15+543x^16+272x^17+80x^18+16x^19+2x^20+2x^22

The gray image is a linear code over GF(2) with n=56, k=12 and d=20.
This code was found by Heurico 1.11 in 0.031 seconds.