The generator matrix

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

generates a code of length 61 over Z2[X]/(X^4) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+98x^57+582x^58+676x^59+664x^60+618x^61+493x^62+300x^63+224x^64+138x^65+103x^66+64x^67+102x^68+26x^69+4x^70+1x^72+1x^74+1x^78

The gray image is a linear code over GF(2) with n=488, k=12 and d=228.
This code was found by Heurico 1.16 in 0.922 seconds.