The generator matrix
1 0 0 1 1 1 X 1 1 X 1 X 1 0 1 1 1 0 1 X 1 1 0 X 1 1 1 1 X 0 1 1 1 1 0 0 X X 1 1 1 1 0 0 X X 1 1 X X 1 1 0
0 1 0 0 1 X+1 1 X X+1 1 0 0 1 1 X 0 1 1 X+1 1 0 0 0 0 X X+1 X 1 1 1 X X X X X X X X 1 1 X+1 X+1 1 1 1 1 X+1 X+1 1 1 0 1 1
0 0 1 1 X+1 0 X+1 1 X+1 X X 1 X 1 1 1 X+1 0 X+1 X 0 X 1 1 X+1 0 X+1 X X+1 1 X X 0 0 1 1 1 1 1 1 1 1 X X 0 0 X X 1 1 X+1 0 X+1
0 0 0 X X X 0 0 0 X X X 0 X X 0 0 X X 0 X 0 X 0 X 0 0 X X 0 0 X X 0 X 0 0 X 0 X X 0 X 0 X 0 X 0 0 X 0 X 0
generates a code of length 53 over Z2[X]/(X^2) who´s minimum homogenous weight is 52.
Homogenous weight enumerator: w(x)=1x^0+66x^52+48x^54+6x^56+6x^60+1x^64
The gray image is a linear code over GF(2) with n=106, k=7 and d=52.
As d=52 is an upper bound for linear (106,7,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 7.
This code was found by Heurico 1.16 in 0.0316 seconds.