The generator matrix

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

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+184x^26+340x^27+469x^28+608x^29+804x^30+942x^31+1201x^32+1298x^33+1384x^34+1492x^35+1544x^36+1454x^37+1168x^38+1070x^39+844x^40+552x^41+384x^42+238x^43+153x^44+90x^45+44x^46+12x^47+10x^48+8x^49+2x^51+2x^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 29 seconds.