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

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+30x^54+40x^55+97x^56+688x^57+97x^58+40x^59+30x^60+1x^114

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 0.219 seconds.