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  X  1  X  1  1  1  1  1  1  1  X  X X^2 X^3 X^2 X^2  X  X  X  X
 0 X^3+X^2  0  0  0 X^2 X^3+X^2 X^2  0 X^3 X^3  0 X^2 X^2 X^3+X^2 X^3+X^2  0 X^3  0 X^2 X^3 X^3+X^2 X^3+X^2 X^2  0 X^2 X^3+X^2 X^3 X^3 X^2 X^3 X^2 X^2 X^2  0 X^2 X^2  0 X^3+X^2  0 X^2 X^3 X^2 X^3+X^2  0 X^3 X^3  0 X^2 X^3+X^2  0 X^3 X^2 X^2  0 X^3 X^3 X^3  0  0
 0  0 X^3+X^2  0 X^2 X^2 X^2 X^3 X^3+X^2 X^3  0 X^2 X^2 X^2  0  0  0 X^3 X^3+X^2 X^3+X^2 X^2 X^2  0 X^3 X^2  0 X^3+X^2  0 X^3+X^2 X^3 X^3 X^3+X^2  0 X^2 X^3  0 X^3+X^2 X^3+X^2  0  0 X^3 X^3+X^2 X^3 X^3  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^3 X^3 X^2 X^3+X^2  0 X^3 X^3  0
 0  0  0 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2  0  0 X^2 X^2  0 X^3+X^2 X^2 X^3  0 X^3+X^2 X^2 X^2 X^3  0 X^3+X^2 X^3 X^3+X^2 X^3+X^2  0 X^3  0 X^3 X^2 X^2 X^3 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^2 X^2  0 X^3  0 X^3  0  0 X^3 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^2
 0  0  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3  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  0  0  0  0  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0  0  0 X^3  0  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3  0  0  0  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+334x^56+64x^57+128x^58+448x^59+128x^60+448x^61+128x^62+64x^63+286x^64+18x^72+1x^96

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 133 seconds.