The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X^2  1  1 X^3+X  1  1  0  1  1 X^2+X  1  1 X^3+X^2  1  1 X^3+X  1  1  0  1  1 X^2+X  1  1 X^3+X^2  1 X^3+X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2+X  1  1 X^3+X^2+X X^3+X  X X^3+X^2  0
 0  1 X+1 X^2+X X^2+1  1 X^3+X^2+X+1 X^3+X^2  1 X^3+X X^3+1  1  0 X+1  1 X^2+X X^2+1  1 X^3+X^2 X^3+X^2+X+1  1 X^3+X X^3+1  1  0 X+1  1 X^2+X X^2+1  1 X^3+X^2 X^3+X^2+X+1  1 X^3+X  1 X^3+1 X^2+1 X+1 X^3+X+1 X^3+X^2+1 X^3+X^2+X+1 X^3+1 X^2+X+1  1 X+1 X^2+1 X^3+X^2+X+1 X^2+1 X^3+X^2+1 X+1 X^3+X+1  0  1 X^3+1 X^3  1  1  1  1  1
 0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3 X^3  0  0  0  0
 0  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3  0  0 X^3 X^3 X^3  0 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0 X^3 X^3  0  0 X^3  0 X^3 X^3  0  0  0 X^3 X^3 X^3  0  0
 0  0  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0  0  0 X^3 X^3 X^3 X^3  0 X^3  0  0  0  0  0 X^3 X^3  0 X^3  0 X^3 X^3  0 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+160x^56+144x^57+225x^58+240x^59+511x^60+240x^61+222x^62+144x^63+156x^64+1x^66+1x^68+1x^72+1x^84+1x^92

The gray image is a linear code over GF(2) with n=480, k=11 and d=224.
This code was found by Heurico 1.16 in 0.172 seconds.