The generator matrix

 1  0  0  0  0  1  1  1  X  1  1  X  1  1  1  0  1  1  X  X  0  1  1  0  1  0  0  0  X  1  0  X  1  1  1
 0  1  0  0  0  0  0  0  0  1  1  1  X  X X+1  1 X+1  1  X  0  X X+1  X  1  0  1  1  0  X X+1  1  X  X  1 X+1
 0  0  1  0  0  0  1  1  1  1 X+1  0  0  1  X X+1  X X+1  1  1  0  X X+1  0  0  X  0  1  X  1  1  1 X+1 X+1  0
 0  0  0  1  0  1  1  X X+1  0 X+1  1  X  X X+1 X+1 X+1  1 X+1  1  1  0  0  0 X+1 X+1  1 X+1  0  0  X  X  0 X+1  0
 0  0  0  0  1  1  X X+1  1  0  1  1  0  1  0  X  X  1  1  0  1  X  X X+1  X  0  X  1  1  1  1 X+1  0  X  0
 0  0  0  0  0  X  0  X  0  X  0  0  X  0  0  X  X  X  X  X  X  0  0  X  0  X  0  0  0  X  X  0  X  0  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+120x^28+296x^30+297x^32+314x^34+346x^36+302x^38+214x^40+102x^42+46x^44+10x^46

The gray image is a linear code over GF(2) with n=70, k=11 and d=28.
This code was found by Heurico 1.16 in 0.24 seconds.