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

generates a code of length 70 over Z2[X]/(X^2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+149x^52+508x^56+889x^60+64x^62+1512x^64+1024x^66+3006x^68+1920x^70+3172x^72+1024x^74+1575x^76+64x^78+880x^80+429x^84+127x^88+31x^92+7x^96+1x^108+1x^120

The gray image is a linear code over GF(2) with n=140, k=14 and d=52.
This code was found by Heurico 1.16 in 65.7 seconds.