The generator matrix

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

generates a code of length 35 over Z2[X]/(X^2) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+86x^25+215x^26+314x^27+501x^28+598x^29+773x^30+898x^31+1144x^32+1350x^33+1388x^34+1596x^35+1467x^36+1438x^37+1326x^38+1042x^39+786x^40+532x^41+347x^42+224x^43+183x^44+84x^45+45x^46+20x^47+13x^48+8x^49+2x^50+2x^51+1x^52

The gray image is a linear code over GF(2) with n=70, k=14 and d=25.
This code was found by Heurico 1.16 in 28.1 seconds.