The generator matrix

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

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+4x^12+28x^13+4x^14+16x^15+3x^16+4x^17+4x^18

The gray image is a linear code over GF(2) with n=56, k=6 and d=24.
This code was found by Heurico 1.16 in 0.000599 seconds.