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

generates a code of length 63 over Z2[X]/(X^4) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+64x^57+133x^58+290x^59+340x^60+430x^61+571x^62+566x^63+592x^64+430x^65+251x^66+142x^67+113x^68+70x^69+34x^70+28x^71+4x^72+10x^73+2x^74+12x^75+5x^76+4x^77+1x^78+2x^79+1x^96

The gray image is a linear code over GF(2) with n=504, k=12 and d=228.
This code was found by Heurico 1.16 in 0.625 seconds.