The generator matrix

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

generates a code of length 35 over Z2[X]/(X^2) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+14x^30+22x^31+39x^32+36x^33+23x^34+26x^35+11x^36+24x^37+17x^38+10x^39+5x^40+4x^41+9x^42+6x^43+5x^44+1x^46+3x^48

The gray image is a linear code over GF(2) with n=70, k=8 and d=30.
This code was found by Heurico 1.16 in 0.016 seconds.