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

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+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 code over GF(2) with n=480, k=11 and d=224.
This code was found by Heurico 1.16 in 0.343 seconds.