The generator matrix

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

generates a code of length 57 over Z2[X]/(X^4) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+718x^51+2230x^52+3716x^53+5203x^54+7442x^55+8946x^56+9196x^57+8846x^58+7804x^59+5179x^60+3396x^61+1769x^62+614x^63+271x^64+116x^65+52x^66+10x^67+13x^68+8x^69+2x^70+4x^71

The gray image is a linear code over GF(2) with n=456, k=16 and d=204.
This code was found by Heurico 1.16 in 32.8 seconds.