The generator matrix
1 0 0 0 0 1 1 1 0 1 1 X 1 0 0 1 1 1 0 1 1 X 0 1 0 0 X 1 1 X X 0 0 1 0
0 1 0 0 0 0 0 0 0 1 1 1 1 1 X X+1 0 X 1 0 1 1 1 X+1 1 0 X X X+1 X 0 1 1 X X
0 0 1 0 0 0 1 1 1 1 X+1 0 0 X+1 X X X 0 1 X+1 X 0 0 X+1 X+1 1 0 1 X 1 1 X 1 1 1
0 0 0 1 0 1 1 0 1 X X+1 1 0 1 1 1 X 1 X+1 1 0 X 1 X+1 X 1 0 0 X+1 X X X+1 X X 1
0 0 0 0 1 1 0 1 X+1 X X+1 X+1 1 X X+1 0 1 0 X+1 1 0 1 X X 0 X 1 X+1 X+1 X 1 X+1 X+1 0 0
0 0 0 0 0 X 0 0 X 0 X X X X 0 0 0 X 0 0 0 X 0 0 0 X X 0 X X 0 0 X 0 0
0 0 0 0 0 0 X 0 0 0 0 0 X 0 X 0 X X X 0 X X 0 X 0 X 0 X X 0 0 X X X 0
0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X X X X X X X
generates a code of length 35 over Z2[X]/(X^2) who´s minimum homogenous weight is 26.
Homogenous weight enumerator: w(x)=1x^0+159x^26+509x^28+817x^30+1176x^32+1417x^34+1428x^36+1248x^38+837x^40+423x^42+127x^44+31x^46+17x^48+1x^50+1x^56
The gray image is a linear code over GF(2) with n=70, k=13 and d=26.
This code was found by Heurico 1.16 in 3.9 seconds.