The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  X  X  X  1  X  1  1  1  1  X  1  1  1  1  1  1  X  X  X  X  X  X  X  X  X  1  1  1  1  1  1  1  1  1  1  X  1
 0 X^3+X^2  0 X^2  0  0 X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^2  0 X^3 X^2 X^3+X^2 X^3 X^2  0 X^3+X^2  0 X^2 X^2 X^2 X^3 X^3+X^2  0 X^2 X^3+X^2 X^3 X^3+X^2 X^3 X^3+X^2  0 X^2 X^3+X^2 X^3  0 X^3+X^2 X^2  0  0 X^3 X^3  0 X^3 X^2 X^3+X^2  0  0 X^2 X^2 X^3+X^2 X^3 X^3+X^2 X^3
 0  0 X^3+X^2 X^2 X^3 X^2 X^3+X^2 X^3 X^3 X^2 X^3+X^2 X^3  0 X^3+X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^3+X^2 X^3 X^3+X^2  0 X^3 X^3+X^2 X^3 X^3+X^2 X^3 X^3+X^2 X^3+X^2  0 X^2 X^3+X^2 X^3 X^2  0 X^2 X^3+X^2 X^2  0 X^3  0 X^3 X^3  0  0 X^2 X^2  0 X^3 X^3+X^2  0 X^3+X^2 X^3+X^2 X^3  0 X^3+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+9x^58+34x^59+173x^60+26x^61+6x^62+2x^63+2x^64+2x^77+1x^86

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 0.141 seconds.