The generator matrix

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

generates a code of length 61 over Z2[X]/(X^4) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+286x^58+332x^59+441x^60+184x^61+315x^62+200x^63+137x^64+24x^65+69x^66+28x^67+21x^68+8x^74+1x^78+1x^82

The gray image is a linear code over GF(2) with n=488, k=11 and d=232.
This code was found by Heurico 1.16 in 0.204 seconds.