The generator matrix

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

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+31x^26+57x^28+69x^30+142x^32+227x^34+216x^36+130x^38+66x^40+37x^42+22x^44+17x^46+7x^48+1x^50+1x^60

The gray image is a linear code over GF(2) with n=70, k=10 and d=26.
This code was found by Heurico 1.16 in 0.116 seconds.