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 X X 0 0 X 1 1 X X 0 1 1 0 X X X 0 1 1 1 1 0 X X X 0 1 1 1 1 X X 0 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 0 X X 1 1 0 X 0 X X X+1 1 1 1 0 X X 0 X X+1 1 1 1 0 X X 0 X X+1 1 0 X X 0
generates a code of length 80 over Z2[X]/(X^2) who´s minimum homogenous weight is 84.
Homogenous weight enumerator: w(x)=1x^0+3x^84+8x^85+3x^86+1x^90
The gray image is a linear code over GF(2) with n=160, k=4 and d=84.
As d=84 is an upper bound for linear (160,4,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.117 seconds.