The generator matrix

 1  0  0  0  1  1  1  1 X^2  0  1 X^2+X  1  1
 0  1  0  0  0 X^2  1 X+1  1  1  X  1 X^2  X
 0  0  1  0  1  X X^2+X X+1 X^2+1  0 X^2+1 X^2+X X^2+X+1 X^2+X
 0  0  0  1  1 X+1  X X^2+X+1 X^2+X  1  X  0 X^2+X X^2+1
 0  0  0  0 X^2  0  0  0  0 X^2 X^2  0 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+294x^10+452x^11+962x^12+1568x^13+1558x^14+1672x^15+1031x^16+384x^17+226x^18+20x^19+22x^20+2x^22

The gray image is a linear code over GF(2) with n=56, k=13 and d=20.
This code was found by Heurico 1.11 in 0.11 seconds.