The generator matrix

1 0 0 0 0 0 0 1 1 1 1 X 1 1 0 X 0 1 1 X 1 0 1 0 X 1 1 X X 0 1 X 1 1 0
0 1 0 0 0 0 0 0 0 0 0 0 0 X 1 1 1 X+1 X 1 X+1 1 X 1 1 X 0 0 X 1 1 X 1 1 0
0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 X X+1 X+1 1 X 0 X 1 X+1 0 X X+1 X 0 0 X+1 1 X 1 1
0 0 0 1 0 0 0 1 0 X X+1 1 X 0 0 1 X+1 0 1 X+1 0 1 X 1 X 0 0 1 X X 1 X+1 0 0 1
0 0 0 0 1 0 0 1 X X+1 X 1 0 0 X 1 1 X+1 X X 1 0 X+1 1 0 X 1 1 1 X+1 1 0 0 X+1 X+1
0 0 0 0 0 1 0 1 X+1 0 X X+1 X 1 1 0 1 1 X X 1 X+1 1 0 0 0 0 X X+1 X 1 0 0 X+1 0
0 0 0 0 0 0 1 X 1 X+1 X+1 X+1 1 X 1 X 1 1 0 X+1 0 X 0 X+1 1 X 1 X+1 X 0 0 1 0 X 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+80x^25+219x^26+312x^27+476x^28+614x^29+796x^30+944x^31+1118x^32+1314x^33+1429x^34+1480x^35+1535x^36+1576x^37+1198x^38+976x^39+796x^40+552x^41+403x^42+240x^43+156x^44+82x^45+46x^46+16x^47+13x^48+6x^49+5x^50+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 1.10 in 4.8 seconds.