The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  X  X  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  X  X  1  X  1
 0  X  0  0  0  0  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  X  X  X  X  X  0  X  0  X  X  X  0
 0  0  X  0  0  0  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  X  X  X  X  X  X  X  X  X  X  X  0  X  X  X  0  0  0  0  X  0  0  X  X  0  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  0  0  X  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  0  0  0  X  0  X  X  0  0  X  X  0  0  X  X  X  0  X  0  X  X  X  0  0  0  X  0  X  0  X  X  X  0  0  X  0
 0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  X  0  0  0  0  0  X  X  X  X  X  X  X  0  0  X  0  0  X  0  0  0  0  X  X  X  X  0  0  X  X  X  0  X  0  0  X  0  X  0  0  X  X  X  X  X  X  X  0  X  X  0  0
 0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  X  0  0  0  0  X  X  X  X  X  X  0  X  X  X  0  0  X  X  X  0  X  X  X  X  0  X  X  0  0  0  X  X  X  X  0  0  0  0  0  X  0  0  0  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  X  0  0  X  X  X  X  X  X  0  X  X  X  0  0  0  0  0  X  X  X  0  X  0  0  0  0  X  X  X  X  X  0  0  X  X  X  X  0  0  X  X  0  0  X  X  X  X  X  0  0  0  X  0
 0  0  0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  0  X  X  0  X  X  0  X  0  X  0  X  X  0  X  0  0  0  X  X  X  0  0  X  0  X  0  0  X  0  0  X  X  0  X  0  X  0  X  X  X  X  X  X  0  X  0  0  0  X  0  X
 0  0  0  0  0  0  0  0  X  0  0  0  0  0  X  0  0  0  0  X  X  X  X  0  X  X  0  0  X  0  X  0  0  0  0  X  X  X  0  X  0  X  X  X  X  0  0  X  X  0  0  0  0  0  X  0  0  0  X  X  X  0  X  0  X  0  0  0  0
 0  0  0  0  0  0  0  0  0  X  0  0  0  X  0  0  0  0  0  X  X  0  X  0  0  0  X  X  X  0  0  X  X  X  X  X  X  0  0  X  X  0  0  X  X  0  0  0  0  0  0  0  0  X  X  X  0  X  X  X  X  X  X  0  0  0  X  0  0
 0  0  0  0  0  0  0  0  0  0  X  0  0  X  0  0  0  0  X  0  0  X  0  X  0  0  X  X  X  X  X  0  0  0  X  X  0  0  X  X  X  X  X  0  X  0  0  0  X  X  0  0  X  X  0  X  X  0  X  X  X  0  0  0  0  X  0  X  X
 0  0  0  0  0  0  0  0  0  0  0  X  0  X  X  X  X  X  X  0  0  0  X  0  0  X  X  X  X  0  X  0  0  X  X  0  0  X  X  0  0  X  X  X  0  0  X  X  0  X  X  0  X  X  X  0  0  0  0  0  X  0  0  X  0  X  0  X  X
 0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  0  0  X  X  X  X  X  0  X  0  X  0  0  X  X  0  X  X  0  X  X  X  X  X  0  0  0  0  0  X  X  0  X  X  X  0  X  0  0  0  X  0  X  0  0  X  X  0  X  X  0

generates a code of length 69 over Z2[X]/(X^2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+233x^52+614x^56+926x^60+64x^62+1680x^64+1344x^66+3643x^68+2240x^70+2777x^72+448x^74+1199x^76+783x^80+320x^84+93x^88+14x^92+4x^96+1x^124

The gray image is a linear code over GF(2) with n=138, k=14 and d=52.
This code was found by Heurico 1.16 in 67.1 seconds.