The generator matrix

1 0 0 0 0 0 0 1 1 1 X 1 1 0 1 1 0 0 1 1 0 1 0 1 X X X X 1 0 0 X 1 1 1 1 1 X 0 1 0 X 0 1 1 0 0 X 1 X 1 X 0 1 1 1 1 1 1 0 1 0 X 1 1 1 0 1
0 1 0 0 0 0 0 0 0 0 0 0 0 0 X X X 1 X+1 1 1 1 1 X+1 1 1 1 0 0 X 0 1 1 1 0 0 1 1 1 X 1 X 1 1 X+1 1 X 0 1 X X 0 0 1 1 X+1 1 1 X+1 1 X+1 1 X 0 X+1 1 0 X
0 0 1 0 0 0 0 0 0 0 0 0 0 X 0 0 X 0 0 0 0 X X X X 0 X X X X X 0 0 X 1 1 X+1 1 1 1 1 1 X+1 X+1 1 1 1 1 X+1 1 1 1 1 1 X 1 X+1 1 X+1 X+1 X+1 0 1 X+1 1 X+1 1 X
0 0 0 1 0 0 0 0 0 X X 1 1 1 1 X+1 1 1 X X+1 1 0 X X+1 X X X+1 0 X 0 1 1 X 1 1 X+1 X 0 0 0 1 1 0 X+1 X 1 0 X+1 0 X X+1 1 X X+1 X+1 X+1 X X 0 0 0 X 0 1 X 1 0 1
0 0 0 0 1 0 0 1 X 1 1 0 X+1 1 0 1 0 1 X 1 X+1 0 0 X 1 1 X 0 X 1 1 X X+1 X 0 1 0 X 0 X+1 1 1 X+1 X+1 1 X 1 0 X+1 1 X X X+1 X+1 0 1 X+1 0 X+1 0 0 X+1 0 1 1 X X+1 0
0 0 0 0 0 1 0 1 X+1 0 1 X X+1 1 1 0 1 X X+1 1 1 0 1 X+1 X 1 X+1 X 1 X X X X X 1 X X+1 X 1 0 0 0 X 0 X+1 1 0 1 1 X+1 X 0 0 1 1 0 0 X+1 X X+1 0 X 1 X X X+1 X 0
0 0 0 0 0 0 1 X 1 1 X+1 1 X+1 0 0 X X+1 0 0 0 X+1 1 1 1 1 X 0 1 X+1 X X+1 X+1 X X X+1 X+1 1 1 X X X+1 X 0 0 X 1 1 X X X+1 0 X+1 1 X+1 1 1 X X 1 0 X 0 0 0 0 X+1 X 1

generates a code of length 68 over Z2[X]/(X^2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+310x^56+714x^58+1110x^60+1380x^62+1768x^64+1832x^66+2046x^68+1998x^70+1831x^72+1412x^74+984x^76+610x^78+241x^80+114x^82+27x^84+4x^86+1x^88+1x^116

The gray image is a linear code over GF(2) with n=136, k=14 and d=56.
This code was found by Heurico 1.10 in 13.5 seconds.