The generator matrix

 1  0  0  1  1  1  X  1  1  1  1 X^2+X  1  1
 0  1  0  1 X^2+X X^2+X+1  1 X^2 X^2+1 X^2+1 X^2+1  1 X^2+X+1  1
 0  0  1  1 X^2+X+1 X^2+X  1  X X+1  0 X^2+X X+1  1  1
 0  0  0 X^2  0  0 X^2  0  0 X^2  0 X^2  0 X^2
 0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2
 0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 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+156x^10+176x^11+566x^12+592x^13+1116x^14+592x^15+575x^16+176x^17+132x^18+10x^20+4x^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 1.16 in 2.23 seconds.