The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X X X X X 0 1 X 0 0 0 0 0 0 1 1 1 0 X 0 X 0 1 1
0 X 0 0 0 X X X 0 0 0 X 0 X X X 0 0 X X 0 X X X 0 X X X X 0 0 0 0 0 0 X X X X X 0 X
0 0 X 0 X X X 0 0 0 X X X X 0 0 0 X X 0 X X 0 0 0 0 0 X X X X 0 0 X X 0 X X X X 0 0
0 0 0 X X 0 X X 0 X X 0 0 X X 0 X X 0 0 0 X X 0 0 0 X X 0 0 X X X X 0 0 0 0 X X 0 X
generates a code of length 42 over Z2[X]/(X^2) who´s minimum homogenous weight is 42.
Homogenous weight enumerator: w(x)=1x^0+22x^42+4x^44+1x^46+3x^48+1x^54
The gray image is a linear code over GF(2) with n=84, k=5 and d=42.
As d=42 is an upper bound for linear (84,5,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 5.
This code was found by Heurico 1.16 in 0.0279 seconds.