The generator matrix

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

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+42x^28+90x^29+92x^30+102x^31+101x^32+82x^33+90x^34+88x^35+70x^36+56x^37+42x^38+54x^39+34x^40+26x^41+30x^42+12x^43+8x^44+2x^45+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 0.0615 seconds.