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

generates a code of length 60 over Z2[X]/(X^4) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+44x^58+64x^59+806x^60+64x^61+44x^62+1x^120

The gray image is a linear code over GF(2) with n=480, k=10 and d=232.
This code was found by Heurico 1.16 in 0.265 seconds.