The generator matrix

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

generates a code of length 14 over Z2[X]/(X^3) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+14x^13+40x^14+7x^16+2x^21

The gray image is a linear code over GF(2) with n=56, k=6 and d=26.
This code was found by an older version of Heurico in 0 seconds.