The generator matrix

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

generates a code of length 60 over Z2[X]/(X^4) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+16x^61+9x^62+4x^63+1x^66+1x^68

The gray image is a linear code over GF(2) with n=480, k=5 and d=244.
This code was found by Heurico 1.16 in 0.109 seconds.