The generator matrix
1 0 1 1 1 0 1 1 0 1 1 0 X 1 1 1 1 0 1 X 1 1 1 0 1 1 1 1 0 1 1 1 X 1
0 1 1 0 1 1 0 1 1 X X+1 1 1 0 X+1 0 X+1 1 X+1 1 X 0 X+1 1 X+1 1 0 X+1 1 X 0 0 X 0
0 0 X 0 0 0 0 0 0 0 X 0 0 X X X X 0 0 0 0 X X X X 0 X 0 0 X 0 X X 0
0 0 0 X 0 0 0 0 0 X 0 0 0 0 X X 0 X X X X X X X X X X X X X 0 0 0 X
0 0 0 0 X 0 0 0 0 0 X X X X 0 X X X X X 0 X X X 0 0 X X 0 0 X 0 0 0
0 0 0 0 0 X 0 0 X 0 0 X 0 X 0 X 0 X 0 0 0 X X X X 0 0 X X 0 0 X 0 X
0 0 0 0 0 0 X 0 X X 0 0 X X 0 0 X 0 X 0 X X X X 0 0 0 0 X 0 0 X X 0
0 0 0 0 0 0 0 X X 0 X 0 X X X 0 0 X 0 X X X 0 X X X 0 0 X 0 X X X X
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+140x^28+98x^30+219x^32+138x^34+186x^36+134x^38+70x^40+14x^42+18x^44+6x^48
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 0.695 seconds.