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 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 1 1 X 1 1 1 1 1 1 X 1 1 1 X 1 1 1 1 X 1 1 X 0 1 1 1 1 1 1 1 1 X 1 1 X 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 X X 0 X X 0 X X 0 X 0 X 0 X X 0 X 0 0 0 X X X 0 X X 0 X 0 X 0 0 X 0 X X X 0 0 0 0 0 X X 0 X 0 0 X 0 X 0 X 0 0 0 0
0 0 X 0 0 0 0 0 0 0 0 X X X X X 0 0 0 X X 0 0 0 0 0 0 X X 0 X X 0 X X X X X 0 0 0 X 0 0 X 0 0 X 0 X X X X X 0 0 X 0 X X X 0 0 X 0 X X X 0 X X X 0 0 X X 0 0 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 0 X 0 X 0 0 0 X X 0 X X 0 0 X X 0 0 X X 0 X 0 0 X X 0 0 0 0 X 0 0 0 X 0 X X X 0 X X X 0 0 0 0 0 0 0 X X 0 0 0
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 X 0 X X 0 X 0 X 0 0 0 X X X X 0 X 0 0 X 0 X X X X X 0 X 0 X X X X 0 0 X 0 X X 0 0 0 X X X 0 0 0 X X 0 0 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 X X X X X 0 X X 0 0 0 X X X 0 X X X 0 X X 0 X 0 X 0 X X X 0 X 0 0 0 X 0 X 0 0 0 X X 0 0 X 0 0 X X 0 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 0 0 X 0 0 0 X X X 0 X 0 X 0 0 0 0 0 X 0 X X X X X X 0 0 X 0 0 0 X 0 0 X 0 X 0 X X X X 0 0 0 X X X X 0 X 0 0 0
0 0 0 0 0 0 0 X 0 X X X X 0 0 0 0 0 X X X X X 0 X X 0 X X X 0 0 0 X 0 0 X 0 X X X 0 0 X 0 X X 0 0 0 0 0 0 X 0 0 0 X 0 X X X X X X 0 0 0 X X 0 0 0 X X 0 X 0 0
0 0 0 0 0 0 0 0 X X X X 0 0 X X X 0 0 0 X 0 0 0 X 0 X 0 0 X X X 0 X X 0 0 0 0 0 X 0 0 X X 0 0 0 0 0 X X 0 0 X X X X 0 X 0 X X X 0 X 0 0 0 X X X 0 X X 0 0 0 0
generates a code of length 79 over Z2[X]/(X^2) who´s minimum homogenous weight is 68.
Homogenous weight enumerator: w(x)=1x^0+58x^68+125x^72+40x^74+178x^76+120x^78+191x^80+88x^82+104x^84+8x^86+52x^88+35x^92+14x^96+8x^100+1x^104+1x^140
The gray image is a linear code over GF(2) with n=158, k=10 and d=68.
This code was found by Heurico 1.16 in 0.387 seconds.