The generator matrix

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

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+261x^10+516x^11+997x^12+1384x^13+1788x^14+1488x^15+1101x^16+408x^17+189x^18+44x^19+13x^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 1.16 in 1.2 seconds.