The generator matrix
1 0 0 1 1 1 X 1 1 X 1 X 1 0 1 1 X 1 X 1 1 1 0 0 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 0 1 1 X 1 0 1 X 1 X X X
0 1 0 0 1 X+1 1 X X+1 1 0 0 1 1 X X+1 1 1 X X 1 X+1 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 1 X+1 1 1 X+1 0 1 X X+1 0 1 1
0 0 1 1 X+1 0 X+1 1 X+1 X X 1 X 1 1 X 1 1 1 0 0 1 1 0 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 0 1 1 X 1 X+1 1 X+1 X X+1 0
0 0 0 X X X 0 0 0 X X X 0 X X X 0 X 0 0 0 0 X X 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 0 0 X X 0 X X X 0 0 X 0
generates a code of length 85 over Z2[X]/(X^2) who´s minimum homogenous weight is 84.
Homogenous weight enumerator: w(x)=1x^0+89x^84+29x^88+6x^92+1x^96+1x^100+1x^104
The gray image is a linear code over GF(2) with n=170, k=7 and d=84.
As d=84 is an upper bound for linear (170,7,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 7.
This code was found by Heurico 1.16 in 0.25 seconds.