The generator matrix
1 0 1 1 1 X 1 1 0 1 1 X 1 1 1 1 0 X 1 X 0 X X 0 X 1 1 1 X 1 0 1 X 1 1 X 0 1 0 1 X 1 1
0 1 X+1 X 1 1 0 X+1 1 X 1 1 0 X X+1 1 1 1 0 X X X X 1 1 X+1 1 X 0 0 1 X 1 X+1 1 0 X 0 1 X 0 X+1 1
generates a code of length 43 over Z2[X]/(X^2) who´s minimum homogenous weight is 45.
Homogenous weight enumerator: w(x)=1x^0+8x^45+4x^46+3x^48
The gray image is a linear code over GF(2) with n=86, k=4 and d=45.
As d=45 is an upper bound for linear (86,4,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.192 seconds.