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 0 0 0 X X 0 1 X+1 1 1 X+1 1 1 1 X X+1 1 0 X 0 1 1 1 X X+1 X 0 0 1
0 0 1 0 0 0 1 X 1 1 1 X+1 X 1 1 X X+1 0 0 X X+1 0 X 0 0 X+1 1 X+1 X X 0 1 X+1 1
0 0 0 1 0 1 X 0 1 X 1 X X+1 0 X+1 1 1 X 0 X 0 0 1 X+1 1 0 0 X X+1 X 1 0 1 X
0 0 0 0 1 X 0 1 1 X+1 1 X+1 X+1 X 1 X 0 1 1 1 1 X X X X+1 X 0 0 X+1 X+1 X+1 X+1 1 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+82x^28+188x^30+208x^32+166x^34+123x^36+112x^38+87x^40+46x^42+11x^44

The gray image is a linear code over GF(2) with n=68, k=10 and d=28.
This code was found by Heurico 1.10 in 0.031 seconds.