The generator matrix
1 0 0 1 1 1 X 1 1 X 1 X 1 0 1 1 X 1 X 1 1 0 0 1 1 X 1 0 1 X 1 1 0 1 1 0 1 X 1 X 1 0 1 1 X 1 1 X X 1 1 1 1 0 0 0 X X X X 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 X 1
0 1 0 0 1 X+1 1 X X+1 1 0 0 1 1 X X+1 1 1 X X 1 1 X X+1 0 1 X 1 0 1 1 0 1 X+1 X 1 X+1 0 X 1 1 0 X 0 X 1 X+1 1 1 X 0 X+1 1 1 1 X 0 0 X X X X 0 0 0 0 X X X X 0 0 1 X+1 X+1 X+1 1 1 X+1 1 1 1 0
0 0 1 1 X+1 0 X+1 1 X+1 X X 1 X 1 1 X 1 1 1 0 0 0 1 1 1 X X X+1 0 1 X+1 X X+1 X+1 X+1 X X 1 X+1 0 0 1 X X+1 1 1 0 0 X+1 0 X+1 1 X X 1 1 0 X X 0 0 X X 0 0 X X 0 1 X+1 X+1 1 1 0 X+1 X X X+1 1 0 0 1 0
0 0 0 X X X 0 0 0 X X X 0 X X X 0 X 0 0 0 X X 0 0 0 X X X X 0 0 0 X X X 0 0 0 0 X X 0 0 X 0 0 X X X X X X 0 0 0 X X X X X X X X 0 0 0 0 0 0 0 0 0 X 0 X X 0 0 X 0 0 X
generates a code of length 83 over Z2[X]/(X^2) who´s minimum homogenous weight is 81.
Homogenous weight enumerator: w(x)=1x^0+12x^81+28x^82+40x^83+28x^84+12x^85+2x^86+1x^96+2x^98+2x^100
The gray image is a linear code over GF(2) with n=166, k=7 and d=81.
This code was found by Heurico 1.16 in 0.105 seconds.