The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  X  1  1  1  X  1  1  1  1  1  1  1  1  0  1  X  1  1  1  1 X^3 X^2  1 X^3+X^2  X  1  0  0  1 X^3 X^3
 0  X  0 X^3+X^2+X X^2 X^2+X X^3+X^2  X  0 X^2+X X^3 X^2+X X^3+X X^2 X^2  X  0 X^2+X X^2 X^3+X  0 X^3+X  0 X^3+X X^3+X  X X^3+X^2+X X^3+X^2 X^3+X^2 X^3+X^2 X^2+X X^3+X^2 X^3+X  X X^3+X X^2+X  X X^3+X X^3+X^2+X  X X^3+X^2  X X^3+X^2+X X^3+X^2+X X^3+X^2 X^3  X X^2 X^3+X  X X^3+X  X  X  X  0  X  X
 0  0 X^3+X^2  0 X^2  0 X^3  0 X^2 X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2  0 X^2  0 X^3+X^2 X^3 X^3+X^2 X^2  0 X^2 X^3 X^2 X^3+X^2 X^2 X^2  0 X^2 X^3  0 X^3 X^3 X^3 X^2  0 X^3+X^2 X^3+X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3  0  0 X^2 X^3+X^2 X^2 X^3 X^3+X^2  0 X^3 X^2 X^2  0
 0  0  0 X^3+X^2  0 X^3 X^3 X^2 X^2 X^2 X^2  0  0 X^2 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2 X^3 X^2 X^3 X^3 X^2 X^3 X^2  0  0  0 X^2  0 X^2 X^3 X^2 X^3+X^2 X^2  0 X^3+X^2 X^2 X^3  0  0 X^3 X^2 X^2  0 X^3+X^2 X^3 X^3  0  0 X^3 X^2 X^3 X^3+X^2 X^3 X^2
 0  0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0  0  0  0  0  0 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+325x^52+528x^54+128x^55+1036x^56+256x^57+816x^58+128x^59+628x^60+160x^62+59x^64+23x^68+7x^72+1x^88

The gray image is a linear code over GF(2) with n=456, k=12 and d=208.
This code was found by Heurico 1.16 in 35.6 seconds.