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 X^3  1  1  1  1  1  1  X
 0  X X^3+X^2 X^2+X  0 X^2+X X^3+X^2 X^3+X  0 X^2+X X^3+X X^3+X^2 X^3 X^3+X^2+X X^2 X^3+X  0 X^2+X X^3+X^2 X^3+X  0 X^2+X X^3+X^2 X^3+X  0 X^2+X X^3+X^2 X^3+X X^3+X^2+X  0  X X^3+X^2 X^3 X^2 X^2+X X^3+X^2+X X^3 X^3+X  X X^2 X^2+X X^3+X^2+X X^3+X  X  0  0 X^3  0 X^3 X^3 X^3+X X^3+X X^3  X  X X^2+X X^3+X^2 X^3+X^2 X^2 X^2+X
 0  0 X^3  0  0  0 X^3  0  0  0  0 X^3  0  0 X^3  0  0 X^3  0 X^3  0 X^3  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 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3  0  0  0  0 X^3 X^3
 0  0  0 X^3  0  0  0 X^3  0  0  0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3  0 X^3  0  0  0  0  0 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3  0  0 X^3  0  0 X^3 X^3  0
 0  0  0  0 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3  0 X^3  0 X^3  0  0
 0  0  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3 X^3 X^3  0  0  0  0 X^3  0  0 X^3  0 X^3  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0 X^3  0 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+85x^56+128x^57+320x^58+384x^59+339x^60+512x^61+48x^62+54x^64+128x^65+48x^66+1x^116

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 0.344 seconds.