The generator matrix
1 0 0 1 1 1 X 1 1 X 1 X 1 0 1 1 1 1 1 1 X 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X
0 1 0 0 1 X+1 1 X X+1 1 0 0 1 1 X X X 0 0 1 1 X X+1 1 X+1 0 1 1 X 1 X+1 X+1 1 1 X X+1 0 0 X X+1 1 1
0 0 1 1 X+1 0 X+1 1 X+1 X X 1 X 1 1 X+1 X+1 1 0 1 X+1 X X+1 X+1 0 X X+1 X X 1 X X 0 0 0 1 X+1 X+1 0 1 1 1
0 0 0 X X X 0 0 0 X X X 0 X X 0 X 0 X X X X X X 0 0 0 X 0 0 X 0 X 0 X X 0 X 0 0 0 X
generates a code of length 42 over Z2[X]/(X^2) who´s minimum homogenous weight is 40.
Homogenous weight enumerator: w(x)=1x^0+32x^40+64x^42+24x^44+6x^48+1x^64
The gray image is a linear code over GF(2) with n=84, k=7 and d=40.
As d=40 is an upper bound for linear (84,7,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 7.
This code was found by Heurico 1.16 in 0.0147 seconds.