The generator matrix

 1  0  1  1  1 3X+2  1  1  2  1  1 3X  1  1  0  1  1 3X+2  1  1  2  1  1 3X  1  1  0  1  1 3X+2  1  1  2  1 3X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 3X+2  1  1 X+2 3X  X  2  0
 0  1 X+1 3X+2 2X+3  1 X+3  2  1 3X 2X+1  1  0 X+1  1 3X+2 2X+3  1  2 X+3  1 3X 2X+1  1  0 X+1  1 3X+2 2X+3  1  2 X+3  1 3X  1 2X+1 2X+3 X+1 3X+1  3 X+3 2X+1 3X+3  1 X+1 2X+3 X+3 2X+3  3 X+1 3X+1  0  1 2X+1 2X  1  1  1  1  1
 0  0 2X  0  0  0  0 2X 2X 2X 2X 2X  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X  0  0  0 2X 2X 2X  0 2X  0 2X 2X  0  0  0 2X 2X  0  0 2X  0 2X 2X  0 2X  0 2X  0 2X  0  0 2X 2X  0  0  0  0
 0  0  0 2X  0 2X 2X 2X 2X  0 2X  0 2X  0 2X  0 2X  0  0 2X  0 2X  0 2X  0  0 2X 2X 2X  0 2X  0  0  0 2X 2X  0 2X 2X  0  0 2X  0  0 2X 2X  0  0 2X  0 2X 2X  0  0  0 2X 2X 2X  0  0
 0  0  0  0 2X  0 2X 2X 2X 2X  0 2X  0 2X  0  0 2X  0 2X  0 2X 2X  0 2X 2X  0 2X  0 2X  0 2X 2X 2X  0  0  0  0  0 2X 2X 2X 2X  0 2X  0  0  0  0  0 2X 2X  0 2X  0 2X 2X  0 2X  0 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+160x^56+144x^57+225x^58+240x^59+511x^60+240x^61+222x^62+144x^63+156x^64+1x^66+1x^68+1x^72+1x^84+1x^92

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 0.156 seconds.