The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X^2  1 X^3+X  1  1  1  0  1  1 X^2+X X^3+X^2  1  1  1  1 X^3+X  1  1  0  1  1 X^2+X X^3+X  1  1  1 X^3+X^2  1  1  1  0  1  1 X^2+X  X  1  1  1  1  1 X^3+X^2 X^3+X^2  1  1  X  1  1  1  X  1  1  1  1 X^2+X X^3+X^2+X
 0  1 X+1 X^2+X X^2+1  1 X^3+X^2 X^3+X^2+X+1  1 X^3+X  1 X^3+1  0 X+1  1 X^2+X X^2+1  1  1 X^3+X^2 X^3+X^2+X+1 X^3+X X^3+1  1 X^2+X X+1  1 X^3+X^2 X^2+1  1  1  0 X^3+1 X^3+X  1 X^2+1 X^3+X^2+X+1  0  1 X^2+X X+1  1  0 X^3 X^3+X^2+X X^3+X X^3+X^2 X^3+X^2  1  1 X^3+X^2+X+1  X X^3+X X^3+X^2+1 X^2+X X+1  X X^3+X  X X^3+1 X^3+X^2+X  1  1
 0  0 X^3  0  0  0  0  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3  0  0  0 X^3 X^3 X^3  0
 0  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0 X^3 X^3  0  0 X^3  0 X^3  0  0 X^3
 0  0  0  0 X^3  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0  0  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0  0  0  0
 0  0  0  0  0 X^3 X^3 X^3 X^3  0 X^3  0  0  0 X^3  0 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3  0  0  0 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+145x^58+176x^59+553x^60+336x^61+623x^62+480x^63+581x^64+416x^65+478x^66+112x^67+137x^68+16x^69+32x^70+5x^72+1x^78+1x^80+2x^84+1x^90

The gray image is a linear code over GF(2) with n=504, k=12 and d=232.
This code was found by Heurico 1.16 in 0.344 seconds.