The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+114x^60+4x^62+3x^64+4x^66+2x^68

The gray image is a linear code over GF(2) with n=480, k=7 and d=240.
This code was found by Heurico 1.16 in 0.109 seconds.