The generator matrix

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

generates a code of length 34 over Z2[X]/(X^2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+88x^28+182x^30+194x^32+178x^34+133x^36+108x^38+85x^40+42x^42+11x^44+2x^46

The gray image is a linear code over GF(2) with n=68, k=10 and d=28.
This code was found by Heurico 1.16 in 0.0616 seconds.