The generator matrix

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

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+286x^51+1074x^52+1990x^53+2596x^54+3736x^55+4572x^56+4728x^57+4159x^58+3994x^59+2488x^60+1626x^61+886x^62+328x^63+165x^64+56x^65+45x^66+24x^67+10x^68+2x^72+2x^74

The gray image is a linear code over GF(2) with n=456, k=15 and d=204.
This code was found by Heurico 1.16 in 10.7 seconds.