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

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+188x^57+96x^58+348x^59+160x^60+520x^61+182x^62+296x^63+44x^64+140x^65+25x^66+28x^67+2x^68+16x^69+1x^74+1x^104

The gray image is a linear code over GF(2) with n=488, k=11 and d=228.
This code was found by Heurico 1.16 in 0.39 seconds.