The generator matrix

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

generates a code of length 35 over Z2[X]/(X^2) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+16x^25+119x^26+150x^27+228x^28+328x^29+411x^30+466x^31+607x^32+662x^33+678x^34+784x^35+716x^36+732x^37+598x^38+536x^39+388x^40+280x^41+227x^42+106x^43+92x^44+28x^45+15x^46+6x^47+12x^48+2x^49+4x^52

The gray image is a linear code over GF(2) with n=70, k=13 and d=25.
This code was found by Heurico 1.16 in 3.78 seconds.