The generator matrix

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

generates a code of length 57 over Z2[X]/(X^4) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+423x^50+1632x^51+4133x^52+6684x^53+10668x^54+14578x^55+17357x^56+19284x^57+18500x^58+14936x^59+10935x^60+6164x^61+3358x^62+1452x^63+584x^64+252x^65+71x^66+40x^67+12x^68+2x^70+2x^71+2x^72+2x^74

The gray image is a linear code over GF(2) with n=456, k=17 and d=200.
This code was found by Heurico 1.16 in 111 seconds.