The generator matrix

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

generates a code of length 35 over Z2[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+52x^24+72x^25+151x^26+104x^27+198x^28+308x^29+346x^30+488x^31+571x^32+656x^33+694x^34+784x^35+726x^36+712x^37+596x^38+528x^39+400x^40+264x^41+224x^42+136x^43+82x^44+36x^45+34x^46+8x^47+16x^48+2x^50+2x^52+1x^58

The gray image is a linear code over GF(2) with n=70, k=13 and d=24.
This code was found by Heurico 1.16 in 3.44 seconds.