The generator matrix

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

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+108x^58+250x^59+337x^60+220x^61+83x^62+10x^63+14x^64+1x^114

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 14.6 seconds.