The generator matrix

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

generates a code of length 57 over Z2[X]/(X^4) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+360x^52+1018x^53+1591x^54+2106x^55+2460x^56+2106x^57+2088x^58+1834x^59+1239x^60+742x^61+451x^62+214x^63+93x^64+38x^65+19x^66+6x^67+15x^68+2x^70+1x^74

The gray image is a linear code over GF(2) with n=456, k=14 and d=208.
This code was found by Heurico 1.16 in 4.47 seconds.