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

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

Homogenous weight enumerator: w(x)=1x^0+14x^56+8x^57+31x^58+120x^59+676x^60+120x^61+31x^62+8x^63+13x^64+1x^66+1x^118

The gray image is a code over GF(2) with n=480, k=10 and d=224.
This code was found by Heurico 1.16 in 0.204 seconds.