The generator matrix

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

generates a code of length 60 over Z2[X]/(X^4) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+535x^56+864x^57+1452x^58+922x^59+1419x^60+792x^61+798x^62+424x^63+496x^64+200x^65+171x^66+54x^67+40x^68+8x^69+10x^70+4x^72+1x^74+1x^76

The gray image is a linear code over GF(2) with n=480, k=13 and d=224.
This code was found by Heurico 1.16 in 19.6 seconds.