The generator matrix

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

generates a code of length 69 over Z2[X]/(X^2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+44x^54+30x^55+158x^56+112x^57+274x^58+272x^59+392x^60+424x^61+578x^62+670x^63+721x^64+924x^65+894x^66+1034x^67+1048x^68+1188x^69+1002x^70+1112x^71+931x^72+904x^73+792x^74+740x^75+559x^76+432x^77+352x^78+198x^79+197x^80+108x^81+118x^82+34x^83+76x^84+4x^85+38x^86+6x^87+7x^88+2x^90+4x^92+2x^94+1x^96+1x^108

The gray image is a linear code over GF(2) with n=138, k=14 and d=54.
This code was found by Heurico 1.16 in 43.3 seconds.