The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X 1 1 1 X X X 1 1 1 1 X X^2 X^2 X^2 X X X X 1 1 1 1 X X X X X X X X X X^2
0 X^3 0 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 0
0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 0 0
generates a code of length 52 over Z2[X]/(X^4) who´s minimum homogenous weight is 52.
Homogenous weight enumerator: w(x)=1x^0+56x^52+5x^56+2x^68
The gray image is a linear code over GF(2) with n=416, k=6 and d=208.
This code was found by Heurico 1.16 in 0.062 seconds.