The generator matrix

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

generates a code of length 57 over Z2[X]/(X^4) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+622x^53+714x^54+1272x^55+1132x^56+1406x^57+853x^58+868x^59+421x^60+494x^61+135x^62+160x^63+61x^64+34x^65+8x^66+4x^67+1x^68+4x^69+1x^70+1x^74

The gray image is a linear code over GF(2) with n=456, k=13 and d=212.
This code was found by Heurico 1.16 in 110 seconds.