The generator matrix

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

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+78x^27+157x^28+204x^29+228x^30+252x^31+307x^32+336x^33+354x^34+304x^35+300x^36+348x^37+328x^38+264x^39+227x^40+184x^41+108x^42+58x^43+31x^44+16x^45+4x^46+4x^47+2x^50+1x^56

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 1.1 seconds.