The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  1  1  1  X  1  X  1  X  X  1 X^2  1  0  X X^2  X X^3  1  X  X  1 X^2  X  X  X  X  1  1  1 X^2 X^2  0  0 X^3 X^3 X^2
 0 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3+X^2 X^2 X^3 X^2  0 X^3+X^2 X^3+X^2 X^3 X^2 X^2  0 X^3  0 X^3+X^2 X^3 X^2 X^3+X^2 X^2 X^2 X^2 X^3+X^2  0 X^3 X^2 X^3  0 X^3 X^3+X^2 X^2  0 X^3 X^3+X^2  0 X^3+X^2 X^3 X^2 X^2 X^3 X^2

generates a code of length 57 over Z2[X]/(X^4) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+40x^57+2x^58+16x^59+2x^60+2x^62+1x^64

The gray image is a linear code over GF(2) with n=456, k=6 and d=228.
This code was found by Heurico 1.16 in 0.094 seconds.