The generator matrix

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

generates a code of length 63 over Z2[X]/(X^4) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+908x^60+228x^61+1138x^62+152x^63+813x^64+48x^65+375x^66+72x^67+252x^68+12x^69+86x^70+8x^72+2x^80+1x^82

The gray image is a linear code over GF(2) with n=504, k=12 and d=240.
This code was found by Heurico 1.16 in 29.5 seconds.