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  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X X^2  X  X  X X^2  1  1
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3 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^3+X^2 X^3+X^2 X^2  0  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3+X^2 X^2 X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^3+X^2  0  0
 0  0 X^3  0  0  0 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0  0  0  0  0  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  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  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0  0  0  0
 0  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3  0  0  0  0  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+12x^56+108x^58+284x^60+80x^62+19x^64+2x^66+4x^68+2x^82

The gray image is a linear code over GF(2) with n=480, k=9 and d=224.
This code was found by Heurico 1.16 in 0.172 seconds.