The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 X X X X 1 1 1 1 1 1 1
0 X 0 0 0 0 0 0 0 0 0 X 0 0 X X 0 0 0 0 X X 0 X X X X X X 0 0 0 X 0 0
0 0 X 0 0 0 0 0 0 0 0 X X X X X 0 0 0 X X 0 X 0 0 0 X 0 X X 0 0 0 X 0
0 0 0 X 0 0 0 0 0 0 X 0 X X 0 X X 0 X 0 X X X X X X 0 0 X 0 0 0 0 0 X
0 0 0 0 X 0 0 0 0 0 X 0 0 X X X X X 0 X 0 0 0 0 0 X 0 0 X X X X X X 0
0 0 0 0 0 X 0 0 0 X 0 0 0 X X 0 X 0 X X X 0 0 X 0 X X X 0 X X 0 X X 0
0 0 0 0 0 0 X 0 0 X 0 0 X 0 0 X X X 0 X X 0 X X X 0 X 0 0 0 0 0 0 X X
0 0 0 0 0 0 0 X 0 X X X X 0 0 0 0 0 X X X X 0 0 X X X X 0 0 X X 0 0 0
0 0 0 0 0 0 0 0 X X X X 0 0 X X X 0 0 0 X 0 X 0 X 0 0 0 0 X X X 0 0 0
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+31x^26+57x^28+69x^30+142x^32+227x^34+216x^36+130x^38+66x^40+37x^42+22x^44+17x^46+7x^48+1x^50+1x^60
The gray image is a linear code over GF(2) with n=70, k=10 and d=26.
This code was found by Heurico 1.16 in 0.116 seconds.