The generator matrix

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

generates a code of length 60 over Z2[X]/(X^4) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+70x^56+304x^57+209x^58+334x^59+232x^60+364x^61+184x^62+256x^63+49x^64+20x^65+19x^66+2x^67+3x^74+1x^98

The gray image is a linear code over GF(2) with n=480, k=11 and d=224.
This code was found by Heurico 1.16 in 0.219 seconds.