The generator matrix

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

generates a code of length 35 over Z2[X]/(X^2) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+126x^26+536x^28+868x^30+1200x^32+1306x^34+1452x^36+1250x^38+824x^40+456x^42+140x^44+26x^46+5x^48+2x^56

The gray image is a linear code over GF(2) with n=70, k=13 and d=26.
This code was found by Heurico 1.10 in 1.3 seconds.