The generator matrix

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

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+374x^57+1206x^58+2062x^59+2952x^60+3534x^61+4304x^62+4342x^63+4336x^64+3584x^65+2568x^66+1656x^67+927x^68+458x^69+280x^70+94x^71+55x^72+14x^73+10x^74+6x^75+1x^76+4x^77

The gray image is a linear code over GF(2) with n=504, k=15 and d=228.
This code was found by Heurico 1.16 in 13 seconds.