The generator matrix

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

generates a code of length 68 over Z2[X]/(X^2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+78x^52+163x^54+349x^56+516x^58+861x^60+1299x^62+1733x^64+2146x^66+2137x^68+2099x^70+1776x^72+1290x^74+859x^76+512x^78+282x^80+142x^82+93x^84+22x^86+19x^88+2x^90+4x^92+1x^110

The gray image is a linear code over GF(2) with n=136, k=14 and d=52.
This code was found by Heurico 1.16 in 47.8 seconds.