The generator matrix

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

generates a code of length 35 over Z2[X]/(X^2) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+70x^27+156x^28+210x^29+256x^30+246x^31+295x^32+312x^33+298x^34+366x^35+350x^36+318x^37+344x^38+282x^39+182x^40+166x^41+117x^42+60x^43+38x^44+16x^45+8x^46+2x^48+2x^49+1x^58

The gray image is a linear code over GF(2) with n=70, k=12 and d=27.
This code was found by Heurico 1.16 in 1.12 seconds.