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 X^3+X^2  1  1  1  1  1  1  X  1  X  1  1  1  1  1  1  1 X^3+X^2  X  1  1 X^3+X^2  X X^3  1  1
 0  X  0  X X^3  0 X^3+X  X X^2 X^2+X X^2 X^2+X X^3+X^2 X^3+X^2+X X^2 X^2+X  0 X^3 X^3+X X^3+X  0 X^2 X^3+X X^2+X X^2 X^3+X^2+X X^3 X^2+X X^3+X^2 X^2+X X^3+X^2  X  0 X^2  X  X X^3+X^2 X^3+X X^3+X X^3+X^2+X X^2 X^3+X X^3+X^2+X X^3+X  X X^2  0 X^2+X  X X^3+X^2  0  X  X X^3  X  0 X^3  X X^3+X^2 X^3+X
 0  0  X  X X^2 X^2+X X^2+X X^2 X^2 X^3+X^2+X  X X^3+X^2  0 X^3+X X^2+X X^3  0 X^3+X^2+X X^2+X X^3+X^2 X^3+X^2 X^2+X X^3+X X^3+X^2 X^3+X^2 X^3+X^2+X X^3+X X^3 X^3 X^3+X X^3+X  0 X^3 X^3+X X^2+X X^3+X^2+X X^2+X X^3+X X^2 X^3+X^2  0 X^2+X  0 X^3 X^2+X  0 X^2 X^3+X X^3+X^2  X  X X^3 X^2  X X^3+X^2+X  X X^3+X  X X^2 X^2
 0  0  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3  0 X^3 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+162x^56+112x^57+275x^58+340x^59+354x^60+350x^61+194x^62+76x^63+102x^64+16x^65+43x^66+20x^68+2x^69+1x^104

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 0.281 seconds.