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

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+157x^56+560x^58+523x^60+512x^61+72x^62+118x^64+104x^66+1x^116

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 1.52 seconds.