The generator matrix

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

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+70x^58+119x^60+52x^62+4x^64+6x^66+1x^68+3x^72

The gray image is a linear code over GF(2) with n=480, k=8 and d=232.
This code was found by Heurico 1.16 in 0.171 seconds.