The generator matrix

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

generates a code of length 57 over Z2[X]/(X^4) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+348x^54+256x^55+396x^56+152x^57+376x^58+216x^59+208x^60+8x^61+54x^62+8x^63+17x^64+4x^66+2x^70+1x^72+1x^88

The gray image is a linear code over GF(2) with n=456, k=11 and d=216.
This code was found by Heurico 1.16 in 79.3 seconds.