The generator matrix

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

generates a code of length 35 over Z2[X]/(X^2) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+40x^26+64x^27+138x^28+198x^29+237x^30+252x^31+273x^32+288x^33+353x^34+392x^35+345x^36+380x^37+262x^38+256x^39+208x^40+144x^41+118x^42+56x^43+52x^44+14x^45+13x^46+4x^47+6x^48+1x^50+1x^52

The gray image is a linear code over GF(2) with n=70, k=12 and d=26.
This code was found by Heurico 1.16 in 0.922 seconds.