The generator matrix

 1  0  0  1  1  1 X^3  1  1  1  1 X^2  0  0  1 X^3+X  1  1  1 X^2+X  X  1  1  X X^2+X  1 X^3+X  1  1  1 X^2  1 X^2+X  1 X^2+X  1 X^3+X^2+X X^3 X^3+X^2  1 X^3+X^2+X X^2+X X^3+X^2  1 X^2  1 X^2+X  0  1  1  1  1  1  1  0  1  1
 0  1  0 X^3 X^2+1 X^3+X^2+1  1  X X^3+X X^3+X^2+X+1 X^2+X+1  1  1 X^2+X X^3+X^2  1 X^3+X+1 X^3+1 X^3  0  1 X^2+1  1  1  1 X^3+X^2  X X^3+X^2+X X^2+X+1 X^3+X  1  X X^3+X^2  0  1 X^3+X^2+X  1  1  1 X^3+X^2  1  1 X^2 X+1  1  1  1  1 X^2+1  1 X+1  X X+1 X^3  X X^3+X^2 X^3
 0  0  1 X^3+X+1 X+1 X^3 X^3+X+1 X^3+X X^3+1  1  X  1 X^3+X  1 X^2+X X^3+X^2+X X^3+X^2+X+1  X X^3+X^2+1  1  1  1 X^3 X+1 X^3+X^2 X^2  1 X^2+1 X^3+X^2 X^3+X^2+X+1 X^2 X^3+X^2  1 X^3+X^2+X X^3+X^2+X X^3+X^2+X+1  1 X^2+1 X^3+X X^2+X+1 X^3+X+1 X^2+X+1  1 X+1 X^2+X X+1  0 X^2+X+1 X^2+X X^3+X^2+1  1  0 X^3+X^2+X X^3+X^2+X+1  1 X^2+1 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+84x^53+528x^54+592x^55+884x^56+560x^57+488x^58+308x^59+240x^60+112x^61+149x^62+60x^63+67x^64+12x^65+10x^66+1x^70

The gray image is a linear code over GF(2) with n=456, k=12 and d=212.
This code was found by Heurico 1.16 in 0.766 seconds.