The generator matrix

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

generates a code of length 67 over Z2[X]/(X^2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+208x^52+40x^54+580x^56+416x^58+1342x^60+1186x^62+2343x^64+1950x^66+2588x^68+1596x^70+1867x^72+796x^74+889x^76+154x^78+307x^80+6x^82+92x^84+21x^88+1x^96+1x^108

The gray image is a linear code over GF(2) with n=134, k=14 and d=52.
This code was found by Heurico 1.16 in 52.1 seconds.