The generator matrix

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

generates a code of length 35 over Z2[X]/(X^2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+107x^28+288x^30+343x^32+308x^34+343x^36+274x^38+215x^40+112x^42+46x^44+10x^46+1x^48

The gray image is a linear code over GF(2) with n=70, k=11 and d=28.
This code was found by Heurico 1.10 in 0.094 seconds.