The generator matrix

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

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+20x^54+64x^55+110x^56+640x^57+104x^58+64x^59+16x^60+4x^62+1x^112

The gray image is a linear code over GF(2) with n=456, k=10 and d=216.
This code was found by Heurico 1.16 in 33.7 seconds.