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

generates a code of length 62 over Z2[X]/(X^4) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+164x^57+252x^58+322x^59+493x^60+586x^61+644x^62+600x^63+429x^64+184x^65+161x^66+96x^67+24x^68+74x^69+30x^70+16x^71+12x^72+1x^74+6x^75+1x^100

The gray image is a linear code over GF(2) with n=496, k=12 and d=228.
This code was found by Heurico 1.16 in 0.5 seconds.