The generator matrix

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

generates a code of length 67 over Z2[X]/(X^2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+69x^54+140x^55+233x^56+358x^57+436x^58+540x^59+611x^60+724x^61+794x^62+826x^63+943x^64+974x^65+986x^66+1070x^67+1062x^68+928x^69+938x^70+918x^71+792x^72+762x^73+653x^74+522x^75+361x^76+240x^77+183x^78+116x^79+83x^80+42x^81+33x^82+28x^83+8x^84+4x^85+4x^86+1x^92+1x^100

The gray image is a linear code over GF(2) with n=134, k=14 and d=54.
This code was found by Heurico 1.16 in 73.7 seconds.