The generator matrix
1 0 1 1 1 X 1 1 0 1 1 X 1 1 0 1 1 X 1 1 1 1 0 X 1 1 1 1 0 X 1 1 1 1 0 X 1 1 1 1 0 X 1 1 1 1 0 X X X 0 1 1 1 1 X X 0 0 X X X 0 1 1 1 1 0 X X X 0 1 1 1 1 X X 0 0 X 1
0 1 X+1 X 1 1 0 X+1 1 X 1 1 0 X+1 1 X 1 1 0 X+1 X 1 1 1 0 X X+1 1 1 1 0 X X+1 1 1 1 0 X X+1 1 1 1 0 X X+1 1 1 1 0 X X 0 X X+1 1 0 X X 1 1 0 X X 0 X X+1 1 1 1 0 X X 0 X X+1 1 0 X X 1 1 0
generates a code of length 82 over Z2[X]/(X^2) who´s minimum homogenous weight is 86.
Homogenous weight enumerator: w(x)=1x^0+2x^86+8x^87+3x^88+2x^90
The gray image is a linear code over GF(2) with n=164, k=4 and d=86.
This code was found by Heurico 1.16 in 0.0935 seconds.