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

generates a code of length 60 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+142x^56+152x^57+275x^58+376x^59+274x^60+364x^61+181x^62+100x^63+81x^64+28x^65+53x^66+4x^67+14x^68+2x^70+1x^102

The gray image is a code over GF(2) with n=480, k=11 and d=224.
This code was found by Heurico 1.16 in 0.282 seconds.