The generator matrix

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

generates a code of length 68 over Z2[X]/(X^2) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+62x^55+152x^56+242x^57+357x^58+416x^59+571x^60+632x^61+748x^62+792x^63+847x^64+930x^65+881x^66+1008x^67+1016x^68+1044x^69+1011x^70+976x^71+855x^72+814x^73+744x^74+534x^75+474x^76+420x^77+311x^78+218x^79+173x^80+70x^81+37x^82+26x^83+7x^84+8x^85+6x^86+1x^114

The gray image is a linear code over GF(2) with n=136, k=14 and d=55.
This code was found by an older version of Heurico in 0 seconds.