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 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
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 0 0 X X X X X X X X 0 0 0 0 1 1 1 1 X+1 X+1 X+1 X+1 X+1 X+1 X+1 X+1 1 1 1 1 0 0 0 X 0 X X X 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 0 X X X X 0 0 1 1 X+1 X+1 X+1 X+1 1 1 1 1 X+1 X+1 X+1 X+1 1 1 0 0 X X X X 0 0 0 0 X X X X 0 0 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 0 X X 0 0 X X 0 0 X X 0 0 X X 0 0 X X 0 0 X X 0 0 X X 0 0 X X 0 0 X X 0 0 X X 0 0
generates a code of length 97 over Z2[X]/(X^2) who´s minimum homogenous weight is 96.
Homogenous weight enumerator: w(x)=1x^0+31x^96+64x^97+28x^98+3x^114+1x^146
The gray image is a linear code over GF(2) with n=194, k=7 and d=96.
As d=96 is an upper bound for linear (194,7,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 7.
This code was found by Heurico 1.16 in 0.191 seconds.