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 1 1 1 1 1 1 1 X X 1 1 X 1 1 1 1 1 X 1 X 1 1 1 1 1 1 X X 0 1 1 1 X X 1 1 1 0 1 1 1 X 1
0 X 0 0 0 0 0 0 0 0 0 0 0 X X X 0 0 0 0 X X X X 0 X X 0 X X 0 X 0 0 0 X X 0 0 X X X 0 X 0 0 X X 0 0 0 X X 0 X X X 0 X X 0 0 X X 0 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 X X X 0 X X X 0 X X 0 0 0 0 0 X X 0 X 0 0 0 0 X 0 X X X 0 0 0 0 0 X X X X X X 0 X 0 0 X X X X 0 0 0 X 0 0 0 X X X 0 0 X X
0 0 0 X 0 0 0 0 0 0 X X X 0 X X 0 X X 0 0 0 0 0 0 0 0 X 0 X X 0 X 0 X X 0 0 X X X X X X 0 0 0 X X 0 X X 0 0 X X X 0 X X X 0 X 0 0 0 0 0 X X 0 0 X X 0 0 0 X
0 0 0 0 X 0 0 0 0 0 X 0 X 0 X 0 X 0 X X X 0 0 X 0 X X X X X X X 0 0 X 0 X X 0 X X 0 0 0 0 0 0 X X X 0 0 0 0 X X X 0 0 0 0 0 0 X X X 0 0 X 0 X 0 X X 0 X 0 X
0 0 0 0 0 X 0 0 0 X 0 0 X 0 0 X X X X 0 X 0 X X 0 X 0 0 X X X 0 X X 0 X 0 X 0 X X X 0 0 0 0 X 0 X X X X X X X X X X 0 X 0 0 0 0 0 X X X X 0 0 X X 0 X 0 0 0
0 0 0 0 0 0 X 0 0 X 0 X 0 X 0 0 0 X 0 0 0 X X X X X 0 0 X 0 X 0 0 0 X X 0 X X X 0 0 X X X X 0 0 0 0 0 0 X 0 X X X 0 X 0 0 X X X X X X 0 0 0 0 X X 0 X 0 0 X
0 0 0 0 0 0 0 X 0 X X X 0 X 0 X 0 0 X X X 0 0 X X X X 0 0 X 0 0 0 0 0 X 0 X X 0 X 0 X 0 0 0 X X 0 0 X 0 0 X 0 X X 0 X 0 X X 0 0 X 0 0 X X X 0 X X 0 0 X 0 X
0 0 0 0 0 0 0 0 X X X 0 0 X X X X X 0 X 0 X 0 X X 0 X 0 X X X 0 X X X X X 0 0 X X X X 0 X X 0 0 X 0 0 X 0 X X 0 0 0 X 0 0 0 X X 0 0 X X X X X X X 0 0 X X X
generates a code of length 78 over Z2[X]/(X^2) who´s minimum homogenous weight is 68.
Homogenous weight enumerator: w(x)=1x^0+71x^68+10x^70+125x^72+144x^74+99x^76+212x^78+66x^80+128x^82+54x^84+18x^86+45x^88+31x^92+19x^96+1x^132
The gray image is a linear code over GF(2) with n=156, k=10 and d=68.
This code was found by Heurico 1.16 in 0.382 seconds.