The generator matrix

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

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+72x^52+24x^53+95x^54+130x^55+320x^56+210x^57+365x^58+488x^59+599x^60+726x^61+748x^62+846x^63+886x^64+1040x^65+996x^66+1132x^67+981x^68+1172x^69+989x^70+930x^71+789x^72+706x^73+550x^74+448x^75+345x^76+190x^77+250x^78+106x^79+81x^80+28x^81+68x^82+12x^83+19x^84+27x^86+4x^87+3x^88+5x^90+2x^94+1x^102

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 38.8 seconds.