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

generates a code of length 70 over Z2[X]/(X^2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+76x^54+160x^56+198x^58+229x^60+334x^62+395x^64+984x^66+959x^68+1368x^70+1373x^72+616x^74+581x^76+264x^78+271x^80+160x^82+85x^84+68x^86+38x^88+26x^90+2x^92+2x^94+1x^96+1x^120

The gray image is a linear code over GF(2) with n=140, k=13 and d=54.
This code was found by Heurico 1.16 in 36.8 seconds.