The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 X 1 1 X 1 1 X X 1 X X^2 X 1 X X^2 X X 1 X^3 X 0 X^2 X^2 X X^2 X X^3 1 X^2 X^3 0
0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 0 0 X^3 X^3 X^3 0 X^3 X^3 0 0 X^3 0 X^3 0 X^3 X^3 0 0 0 X^3 0 X^3 X^3
generates a code of length 52 over Z2[X]/(X^4) who´s minimum homogenous weight is 53.
Homogenous weight enumerator: w(x)=1x^0+20x^53+4x^54+4x^55+3x^56
The gray image is a linear code over GF(2) with n=416, k=5 and d=212.
This code was found by Heurico 1.16 in 0.062 seconds.