The generator matrix

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

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+72x^55+145x^56+260x^57+359x^58+442x^59+552x^60+614x^61+679x^62+798x^63+860x^64+902x^65+1016x^66+988x^67+951x^68+1008x^69+1026x^70+926x^71+927x^72+840x^73+687x^74+642x^75+510x^76+382x^77+275x^78+202x^79+138x^80+78x^81+50x^82+24x^83+11x^84+12x^85+4x^86+2x^87+1x^112

The gray image is a linear code over GF(2) with n=136, k=14 and d=55.
This code was found by Heurico 1.16 in 73.4 seconds.