The generator matrix

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

generates a code of length 35 over Z2[X]/(X^2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+33x^28+34x^29+92x^30+86x^31+84x^32+100x^33+58x^34+106x^35+69x^36+84x^37+62x^38+42x^39+48x^40+36x^41+38x^42+22x^43+17x^44+2x^45+6x^46+3x^48+1x^52

The gray image is a linear code over GF(2) with n=70, k=10 and d=28.
This code was found by Heurico 1.16 in 0.0676 seconds.