The generator matrix

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

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+7x^56+16x^57+16x^58+48x^59+848x^60+48x^61+16x^62+16x^63+7x^64+1x^120

The gray image is a linear code over GF(2) with n=480, k=10 and d=224.
This code was found by Heurico 1.16 in 0.203 seconds.