The generator matrix

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

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+406x^56+320x^57+580x^58+448x^59+622x^60+448x^61+568x^62+320x^63+360x^64+4x^66+2x^68+15x^72+1x^80+1x^88

The gray image is a linear code over GF(2) with n=480, k=12 and d=224.
This code was found by Heurico 1.16 in 24.3 seconds.