The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  X  X  0  0  0  0  0  0  0  X  1  1  1  1
 0  X  0  0  0  X  X  X  0  0  0  X  0  X  X  X  0  0  0  X  X  X  X  X  X  X  X  0  0  0  0  0  0  0  X
 0  0  X  0  X  X  X  0  0  0  X  X  X  X  0  0  0  X  X  X  X  0  0  0  0  X  X  X  X  0  0  0  0  X  X
 0  0  0  X  X  0  X  X  0  X  X  0  0  X  X  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0

generates a code of length 35 over Z2[X]/(X^2) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+4x^34+22x^36+4x^38+1x^40

The gray image is a linear code over GF(2) with n=70, k=5 and d=34.
This code was found by Heurico 1.16 in 0.00424 seconds.