The generator matrix

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

generates a code of length 63 over Z2[X]/(X^4) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+128x^58+544x^59+1028x^60+942x^61+1246x^62+1018x^63+1083x^64+664x^65+622x^66+332x^67+285x^68+150x^69+70x^70+58x^71+10x^72+4x^73+6x^74+1x^76

The gray image is a linear code over GF(2) with n=504, k=13 and d=232.
This code was found by Heurico 1.16 in 1.81 seconds.