The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X^2  1  1 X^3+X  1  1  0  1  1 X^2+X  1  1 X^3+X^2  1  1 X^3+X  1  1  1  1  0 X^2+X  1 X^3+X^2  1 X^3+X  1  1  1  1  1 X^3+X  1  1  1  1  1  X  0 X^3  1  1  1  1  1  1  1 X^3+X^2  1 X^3+X X^2+X X^2 X^3+X^2+X
 0  1 X+1 X^2+X X^2+1  1 X^3+X^2+X+1 X^3+X^2  1 X^3+X X^3+1  1  0 X+1  1 X^2+X X^2+1  1 X^3+X^2 X^3+X^2+X+1  1 X^3+X X^3+1  1  0 X^2+X X+1 X^2+1  1  1 X^3+X^2  1 X^3+X  1 X^3+X^2+X+1 X^3+1 X^2+X X+1 X^2+1  1 X^3+X+1 X^3+X^2+1  0 X^3 X^3+X^2+X  1  1  1 X^3+X^2 X^2 X^3+X  X X^3+X^2 X^2+X X^3+X^2+X+1  1  1  1  1 X^2  1
 0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0  0 X^3 X^3  0 X^3  0 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0  0  0 X^3  0 X^3  0 X^3  0  0 X^3 X^3  0  0  0
 0  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0  0  0 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0  0  0 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0 X^3  0  0 X^3  0  0 X^3 X^3  0  0  0 X^3  0 X^3  0 X^3  0
 0  0  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0  0  0 X^3  0  0  0  0  0 X^3 X^3  0 X^3  0 X^3  0  0 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+152x^57+200x^58+268x^59+269x^60+304x^61+224x^62+296x^63+174x^64+120x^65+24x^66+12x^67+1x^68+1x^76+1x^80+1x^84

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 0.188 seconds.