The generator matrix

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

generates a code of length 61 over Z2[X]/(X^4) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+70x^56+568x^57+818x^58+1370x^59+1013x^60+1268x^61+788x^62+896x^63+476x^64+348x^65+206x^66+230x^67+67x^68+56x^69+12x^70+5x^72

The gray image is a linear code over GF(2) with n=488, k=13 and d=224.
This code was found by Heurico 1.16 in 2.91 seconds.