The generator matrix

 1  0  1  1  1 X^2+X  1  1  1  1  1  1 X^2  1
 0  1 X+1 X^2+X X^2+1  1  0 X^2+X X+1 X^2+1 X^2  X  0 X^2
 0  0 X^2 X^2  0 X^2 X^2  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 12.

Homogenous weight enumerator: w(x)=1x^0+17x^12+46x^13+28x^14+4x^15+14x^16+14x^17+3x^18+1x^22

The gray image is a linear code over GF(2) with n=56, k=7 and d=24.
This code was found by Heurico 1.16 in 0.000767 seconds.